The volume of the square prism with a side of base decreasing at a rate of 7 km/min and height increasing at 10 km/min is decreasing at a rate of 344 cubic km/min.
Explanation:In this problem, we're dealing with rates of change and the geometric properties of a square prism. A square prism can be characterized by the side length of its base (we'll call this length 's') and its height (h). The volume (V) of a square prism is given by the equation V = s^2 * h. We're told that the side length s is decreasing at a rate of 7 kilometers per minute (ds/dt = -7 km/min) and the height h is increasing at a rate of 10 kilometers per minute (dh/dt = 10 km/min).
To find the rate at which the volume is changing with respect to time, we can take the derivative of the volume equation with respect to time. Thus, dV/dt = 2*s*ds/dt*h + s^2*dh/dt. Substituting the given values, when s = 4 km and h = 9 km, we find: dV/dt = 2*4*(-7)*9 + 4^2*10 = -504 + 160 = -344 cubic kilometers per minute. Therefore, at the given instant, the volume of the square prism is decreasing at a rate of 344 cubic kilometers per minute.
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The rate of change of the surface area of the prism at that instant is -204 square kilometers per minute. Correct Option is Option C.
To solve this problem, let's first start by identifying the formula for the surface area (SA) of a square prism, which is given as [tex]2s^2 + 4sh[/tex] , where s is the side of the base and h is the height.
Now, let's find the rate of change of the surface area with respect to time, dSA/dt. We'll use the chain rule to differentiate the surface area formula:
1. Differentiate the given surface area formula:
[tex]SA = 2s^2 + 4sh[/tex]
[tex]d(SA)/dt = d(2s^2)/dt + d(4sh)/dt[/tex]
2. Apply the chain rule:
d(SA)/dt = 2 * 2s * (ds/dt) + 4 * (s * (dh/dt) + h * (ds/dt))
3. Plug in the given values: s = 4 km, ds/dt = -7 km/min, h = 9 km, dh/dt = 10 km/min:
d(SA)/dt = 4 * 4 * (-7) + 4 * (4 * 10 + 9 * (-7))
d(SA)/dt = -112 + 4 * (40 - 63)
d(SA)/dt = -112 + 4 * (-23)
d(SA)/dt = -112 - 92
d(SA)/dt = -204
The rate of change of the surface area of the prism at that instant is -204 square kilometers per minute. Correct Option is Option C.
Complete Question:- The side of the base of a square prism is decreasing at a rate of 7 kilometers per minute and the height of the prism is increasing at a rate of 10 kilometers per minute. At a certain instant, the base's side is 4 kilometers and the height is 9 kilometers. What is the rate of change of the surface area of the prism at that instant (in square kilometers per minute)? Choose 1 answer: A 204 B 148 C -204 D -148 The surface area of a square prism with base side 8 and height h is [tex]2s^2+4sh.[/tex]
The length of the sandbox will be 6 less than 3 times the width. The perimeter of the sandbox must be less than or equal to 116 feet. What would be the maximum length and width of the sandbox.
Answer: the maximum length of the sandbox is 42 feet.
the maximum width of the sandbox is 16 feet.
Step-by-step explanation:
Let L represent the length of the sandbox.
Let W represent the width of the sandbox.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
The perimeter of the sandbox must be less than or equal to 116 feet. This means that
2(L + W) ≤ 116
Dividing through by 2, it becomes
L + W ≤ 116/2
L + W ≤ 58 - - - - - - - - -1
The length of the sandbox will be 6 less than 3 times the width. This means that
L = 3W - 6
Substituting L = 3W - 6 into equation 1, it becomes
3W - 6 + W ≤ 58
4W ≤ 58 + 6
4W ≤ 64
W ≤ 64/4
W ≤ 16
L = 3W - 6 = 3 × 16 - 6
L ≤ 42
In a large class of introductory Statistics students, the professor has each person toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. How much variability would you expect among these proportions?
Answer:
Variability expected among these Proportions is given by Standard deviation = 0.125
Step-by-step explanation:
The probability of tossing heads is the same for a fair coin as the probability of tossing tails.
The probability of tossing heads is then 1 chance out of 2
P = 1/2 = 0.5
The standard deviation of the sample distribution of the sample proportion = √Pq/n
Standard deviation = √p(1-p)/n
= √0.5(1-0.5)/16
Standard deviation = 0.125
The variability among the proportions of heads obtained in the coin tosses is due to the random nature of the experiment. The law of large numbers explains that as the number of tosses increases, the observed relative frequencies of heads will approach the theoretical probability of 0.5.
Explanation:The amount of variability that can be expected among the proportions of heads obtained by the students tossing a coin 16 times can be determined by understanding the concept of probability.
In a single coin toss, the probability of getting a head is 0.5. However, when the coin is tossed more times, the observed proportions of heads will vary from the theoretical probability of 0.5.
The variability among these proportions is attributed to the random nature of the coin tosses and is due to the fact that the short-term results of an experiment do not necessarily match the theoretical probability. The law of large numbers states that as the number of repetitions of an experiment is increased, the observed relative frequencies of heads will tend to become closer to the theoretical probability of 0.5.
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R(x) = -13.85x2 + 1,660x
C(x) = 55,400 – 279x
Answer:
What am I suppose to do?
Step-by-step explanation:
the container that holds the water for the football team is
1/4 full. after pouring in 10 gallons of water, it is 2/3 full.how many gallons can the container hold?No multiple questions at this time
Answer:
The container can hold 24 gallons of water.
Step-by-step explanation:
Let the Amount of water in gallons container can hold be 'x'.
Now given:
the container that holds the water for the football team is 1/4 full.
therefore Amount of water in container = [tex]\frac14x[/tex]
We need to find the Amount of water in gallons container can hold.
Solution:
Now given:
after pouring in 10 gallons of water, it is 2/3 full.
So equation can be framed as;
[tex]\frac14x+10=\frac23x[/tex]
Now Combining the like terms we get;
[tex]10=\frac23x-\frac14x[/tex]
Now We will use LCM to make the denominator common we get;
[tex]10=\frac{2x\times4}{3\times4}-\frac{1x\times3}{4\times3}\\\\10=\frac{8x}{12}-\frac{3x}{12}[/tex]
Now the denominators are common so we will solve the numerator we get;
[tex]10=\frac{8x-3x}{12}\\\\10=\frac{5x}{12}[/tex]
Now Multiplying both side by [tex]\frac{8}{12}[/tex] we get;
[tex]10\times\frac{12}{5}=\frac{5x}{12}\times \frac{12}{5}\\\\x=24 \ gallons[/tex]
Hence The container can hold 24 gallons of water.
Scott purchased a $146,000 home with a 7/23 balloon mortgage. His initial rate was 3.5%. At the end of the initial rate he decided to refinance a balloon payment with a 30 year mortgage fixed at 5%. What is his new mortgage payment
A:$654.87
B:$707.63
C:$655.61
D:$666.55
Answer:D
Step-by-step explanation:
The solution is: : $117,783.05 will be her balloon payment at the end of 7 years if she chooses this mortgage.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
Step 1
Calculate the number of monthly payments for 7 years.
The formula we would be using is given as:
Monthly payment = [Loan amount × (rate/number of year)] ÷ [1 - (1 +r/n)^nt)]
Loan amount =$146,000
Rate = 4.75% = 0.0475
n = number of payments = 12
t= number of years = 23
Monthly payment = [ 146,000× (0.0475/12)] ÷ [1 - (1 +0.0475/12)^-276)]
Monthly payment = $870.49
Step 2
Calculate the amount left after 7 years using the formula
Ballon payment after 7 years = Loan amount ( 1 + r)ⁿ - P[(1 +r)ⁿ - 1 /r]
r = 4.75% for 12 years
= 146,000( 1 + 0.0475/12)^84 - 870.49[((1 + 0.0475/12)^84 - 1)/0.0475/12]
= $117,783.05
Hence, The solution is: : $117,783.05 will be her balloon payment at the end of 7 years if she chooses this mortgage.
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complete question:
Yvette is considering a 7/23 balloon mortgage with an interest rate of 4.75%
to purchase a house for $146,000. What will be her balloon payment at the end of
7 years if she chooses this mortgage?
This little pool is 10 feet in diameter and 3 feet tall. Use the formula for volume to find the total water needed to fill the pool.
V=π r ^2 h
The total water needed to fill the pool is 75π cubic feet.
Given: The pool is 10 feet in diameter and 3 feet tall. To find: The total water needed to fill the pool using V = πr²h formula.
Calculations: Radius (r) = 5 feet, Height (h) = 3 feet. Substitute values into formula: V = π(5)^2(3) = 75π cubic feet.
Answer: The total water needed to fill the pool is 75π cubic feet.
Anna is standing on the roof of a 35-foot building and is located at point A.
There is a 60-foot rope hanging from a point on the roof. When the rope is stretched out, it reaches to point C. She wants to know how far she is from point
B.
If Anna can show that triangles ABD ABD and ACD ACD are congruent, she can find the distance from A to B
Which additional segment lengths could be used to prove that △ADB≅△ADC by using the SAS Congruence Postulate?
THERE IS MORE THAN ONE ANSWER
CD=7 ft.
BD=6 ft.
CD=12 ft.
BD=5 ft.
CD=8 ft.
BD=8 ft.
9514 1404 393
Answer:
CD = 8 ft.
BD = 8 ft.
Step-by-step explanation:
To make use of the SAS postulate, Anna needs to identify two sides on either side of congruent angles.
The only marked angle is the right angle. We know that AD is congruent to itself, so Anna also needs to use the segments CD and BD, which are on the other side of the right angle in the right triangles.
The two choices in which BD and CD have the same length are
CD=8 ft.BD=8 ft.Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward along the z-axis a distance of 5 units. What are the coordinates of your position? (x, y, z)
Answer:
(4,0,-5)
Step-by-step explanation:
Since we move 4 points along +ve x-axis so, x coordinate is 4
We did not move any point along y-axis so y coordinate is 0
we moved 5 points along -ve z-axis so z coordinate is -5
so our position is (x,y,z) = (4,0,-5)
Which of the following describe the function
g(x) = log2 (x - 2) – 3.
Choose ALL that apply.
The domain is the set of all real number greater than 2.
The x-intercept = ( 10,0) and there is no y-intercept
Avertical asymptote at x = 2.
There is no x-intercept and the y-intercept = (0,10 ).
The domain is the set of all real numbers less than 2
The graph of g(x) is symmetric to its inverse exponential function over the line y = 0
The graph of g(x) is symmetric to its inverse exponential function I’ve ether like y = x
A vertical asymptote at x = 10
Answer:
From the plot and from inspection of the equation the following are true
a.) The domain is the set of all real numbers greater than 2
b.) The x-intercept = (10,0) and there is no y-intercept
c.) A vertical asymptote is at x = 2
f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x
Step-by-step explanation:
The plot of the graph is attached.
From the plot and from inspection of the equation the following are true
a.) The domain is the set of all real numbers greater than 2
b.) The x-intercept = (10,0) and there is no y-intercept
c.) A vertical asymptote is at x = 2
f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x
The infant measures 21.5 in (54.6 cm) at birth. If the infant is following a normal pattern of growth, what would be an expected height for the infant at the age of 6 months?
Answer:
27.5 in (69.85 cm)
Step-by-step explanation:
The normal growth rate for an infant after birth is 1 in per month.
After six month, the infant will be 27.5 in which is equivalent to 69.85 cm.
_____ are systematic tendencies to use information about others in ways that result in inaccurate perceptions.
Answer:
biases
Step-by-step explanation
i toke the test
Bias is the systematic tendency to use information about others.
What are systematic tendencies?The propensity to give facts that can be quickly recalled from memory as much weight as possible while making a decision.
You may reap the rewards of group judgments while avoiding frequent challenges to effective judgment in groups by managing group judgment processes well. Fundamental judgment ideas may be learned, but like with other abilities, practice is required. A professional judgment framework is a useful example of a sound decision-making procedure and enables you to identify potential areas for error. A shared framework enables the use of a common language and understanding. It normally pays off to put in some work up front, especially in the initial few stages of the judging process.
Therefore, A few properties of systematic bias are Heuristics are quite effective; typically speaking, benefits outweigh costs; yet, they may lead to biased judgment.
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The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperatures are 40 and 20°C, respectively, has been determined to be 40 W/m2. What is the thermal conductivity of the wood?
Answer:
[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]
Step-by-step explanation:
Previous concepts
The Fourier's law, states that the "rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows".
And we have the following formula given:
[tex] q_x = -k A \frac{dT}{dx}[/tex]
For this case we have the following data given:
[tex] L= 50 mm * \frac{1m}{1000 mm}=0.05m[/tex]
[tex] T_i = 40 C[/tex] represent the inner surface temperature
[tex] T_o = 20 C[/tex] represent the outer surface temperature
[tex] \frac{q_x}{A} = 40 W/m^2 [/tex] represent the heat flux
So then we are interested on the value of k.
Solution to the problem
if we solve for the value of k from the formula:
[tex] q_x = -k A \frac{dT}{dx}[/tex]
We got:
[tex] k = - \frac{q_x}{A \frac{dT}{dx}}[/tex]
We can rewrite this expression like this:
[tex] k = - \frac{q_x}{A \frac{T_o -T_i}{L}}[/tex]
And if we replace the values given we got:
[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]
Using Fourier's law of heat conduction, the thermal conductivity of the wood slab is calculated to be 0.1 W/m·K given a heat flux of 40 W/m², a temperature difference of 20°C, and a thickness of 50 mm.
Explanation:The student is asking about the thermal conductivity of a wood slab, given its thickness, the temperature difference across it, and the heat flux. To find the thermal conductivity (k), we can use Fourier's law of heat conduction which states:
Q/t = k × A × (T2 − T1) / d
where:
Q/t is the rate of heat transfer (40 W/m²),k is the thermal conductivity,A is the cross-sectional area (not needed here as we have heat flux per unit area),(T2 − T1) is the temperature difference across the material (40°C − 20°C = 20°C),d is the thickness of the material (50 mm = 0.05 m).Rearranging the formula to solve for k gives:
k = Q/t × d / (T2 − T1)
Plugging in the values:
k = 40 W/m² × 0.05 m / 20°C
k = 0.1 W/m·K
So, the thermal conductivity of the wood is 0.1 W/m·K.
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Write the slope-intercept form (y=mx+b) of the equation of the line given the slope and y-intercept.
To buy a new guitar, jerry paid a $700 down payment and will pay $50 each month until it is completely paid for. If the total cost of the guitar cost $1,200, how many months will it take to pay for the guitar!
Answer:
Step-by-step explanation:Original price is $1200.and he paid $700 to start with meaning he has $500 more to pay
$1200-$700=$500
If he now pays $50 every months then he has 10months to pay up
$500/$50=10./
The statement "The square of any rational number is rational" can be rewritten formally as "For all rational numbers x, x 2 is rational" or as "For all x, if x is rational then x 2 is rational." Rewrite each of the following statements in the two forms "∀ x, " and "∀x, if , then " or in the two forms "∀ x and y, " and "∀x and y, if , then ."
a. The reciprocal of any nonzero fraction is a fraction.
b. The derivative of any polynomial function is a polynomial function.
c. The sum of the angles of any triangle is 180◦.
d. The negative of any irrational number is irrational.
e. The sum of any two even integers is even.
f. The product of any two fractions is a fraction.
Answer:
a.
For all non zero fraction 1(1/x), 1/x is a fraction
For all 1/(1/x), if 1/(1/x) is non zero, 1/x is a fraction
b.
For all polynomial function f(x) = x³ + x² + x - 1, the derivative (dy/dx) is a polynomial function
For all f(x) x³ + x² + x - 1, if f(x) is polynomial, f'(x) is a polynomial function
c.
For all angles x,y,z of a triangle, the sum, x + y + z = 180
For all x,y,z, if x,y and z are the angles of a triangle, x+y+z = 180
d.
For all irrational numbers x, -x is irrational
For all x, if x is irrational then -x irrational.
e.
For two integers, x and y, the sum x+y is an integer
For x,y if x and y are integers, then x + y is an integer
f.
For two fractions, x/y and a/b the product ax/by is a fraction
For x/y and a/b, if x/y and a/b are fractions then ax/by is a fraction
Final answer:
The statements have been rewritten in both universal quantification and conditional forms to describe relationships in mathematics, such as the property of being a fraction, polynomial function, or summing up to 180 degrees for triangles.
Explanation:
To rephrase the given statements in mathematical terms:
For all nonzero fractions x, if x is a fraction, then 1/x is a fraction.For all polynomial functions f(x), if f(x) is a polynomial function, then f'(x) is a polynomial function.For all triangles, if a figure is a triangle, then the sum of its angles is 180 degrees.For all irrational numbers x, if x is irrational, then -x is irrational.For all even integers m and n, if m and n are even, then m + n is even.For all fractions a and b, if a and b are fractions, then a * b is a fraction.one base of a trapezoid is 3 times the length of the second base. the height of the trapezoid is 2in smaller than the second base if the area is 30 what is the length of both bases
Answer:
Length of bases of the trapezoid are 5 inch and 15 inch.
Step-by-step explanation:
Let the length of the second base be 'x'.
Given:
one base of a trapezoid is 3 times the length of the second base.
So we can say that;
Length of the first base = [tex]3x[/tex]
Also Given:
the height of the trapezoid is 2 in smaller than the second base
So we can say that;
Height of the trapezoid = [tex]x-2[/tex]
Area of the trapezoid = 30
We need to find the length of both the bases.
Solution:
Now we know that;
Area of trapezoid is equal to half of the sum of the length of two bases multiplied by height of the trapezoid.
framing in equation form we get;
[tex]\frac{x+3x}{2}\times(x-2)=30\\\\\frac{4x}{2}\times (x-2)=30\\\\2x(x-2)=30[/tex]
Now Dividing both side by 2 we get;
[tex]\frac{2x}{2}(x-2)=\frac{30}{2}\\\\x(x-2)=15\\\\x^2-2x-15=0[/tex]
Now we will find the roots by factorizing the equation we get;
[tex]x^2-5x+3x-15=0\\\\x(x-5)+3(x-5)=0\\\\(x+3)(x-5)=0[/tex]
Now we find the values of x by solving separately we get;
[tex]x+3=0 \ \ \ \ Or \ \ \ \ \ \ x-5=0\\\\x=-3 \ \ \ \ \ \ \ Or \ \ \ \ \ \ x=5[/tex]
Now we have got 2 values of 'x' one positive and one negative.
Now we know that length of the base of trapezoid cannot be negative hence we will discard it and consider the positive value of 'x'.
Length of second base = 5 in
Length of first base = [tex]3x=3\times5 =15\ in[/tex]
Hence Length of base of the trapezoid are 5 inch and 15 inch.
Use a ruler to measure the side length of the rectangle in centimeters mark 8 cm with a point and connect the points to show the square units then count the squares you're true to find the total area
Answer:
The total area of the rectangle is found by counting the total number of 1 cm squares inside the rectangle.
Note: This question is missing some details.
A more complete question is this: Use a ruler to measure the side lengths of the rectangle in centimeters. Mark each centimeter with a point and connect the points to show the square units. Then, count the squares you drew to find the total area.
Step-by-step explanation:
This method is used to determine area of a rectangle by counting the square unit inside the given rectangle.
For example, if the measurement of the sides of the rectangle is 8 cm and 5 cm respectively. To find the area;
Step 1: Mark out 1 cm points on each side of the rectangle.
Step 2: Connect each of the points.
Step 3: Count the number 1 cm squares within the triangle. The total number of squares gives the area of the triangle.
In this example, the number of 1 cm squares will be found to be 40. So the area of the rectangle is 40 cm squares or 40 cm².
Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be . The actual difference is .
Answer:
Mike estimated the difference to be 72.
The actual difference is 72.74.
Step-by-step explanation:
Mike estimated 79 as 79.44 and 7 as 6.7, therefore Mike estimated the difference, this way:
79 - 7 = 72
Actual difference of the numbers is:
79.44 - 6.7 = 72.74
Mike estimated the difference to be 72.
The actual difference is 72.74.
Perform the indicated operation. (2x + y)(3x2 + y)
WILL CHOOSE FIRST W/ RIGHT ANSWER BRAINLIEST!!!!!!!!
Answer:
Step-by-step explanation:
(2x+y)(3x²+y)=2x(3x²+y)+y(3x²+y)=6x³+2xy+3x²y+y²=6x³+3x²y+2xy+y²
Katy earns $10 per hour. She worked 4 hours on Friday, 9 hours on Saturday, and 6 hours on Sunday. How much money did Katy earn in all on Friday, Saturday, and Sunday? Answer: $
Answer: In total Katy earned $190
Katy earn $190 in all on Friday, Saturday, and Sunday.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS is; Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given that Katy earns $10 per hour. She worked 4 hours on Friday, 9 hours on Saturday, and 6 hours on Sunday.
Therefore, total time = 4+9+6=19
Then 19 x 10 = 190
so, she made $190
Hence, Katy earn $190 in all on Friday, Saturday, and Sunday.
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The annual tuition at a specific college was $20,500 in 2000, and $45,4120
in 2018. Let x be the year since 2000, and y be the tuition. Write an
equation that can be used to find the tuition y for x years after 2000. Use
your equation to estimate the tuition at this college in 2020.
Final answer:
The estimated tuition at this college in 2020 is $51,137.
Explanation:
To find the equation to determine the tuition y for x years after 2000, we need to use the given information: the annual tuition in 2000 was $20,500 and it increased to $45,120 in 2018.
Let's calculate the rate of increase per year:
The change in tuition over the number of years is:
(Tuition in 2018 - Tuition in 2000) / (Year in 2018 - Year in 2000) = (45,120 - 20,500) / (2018 - 2000)
Now, we can use this rate of increase to find the tuition in any given year x:
Tuition in a specific year = Tuition in 2000 + (Rate of increase per year) * x
To estimate the tuition in 2020, we substitute x = 20 into the equation:
Tuition in 2020 = 20,500 + ((45,120 - 20,500) / (2018 - 2000)) * 20 = $51,137
Do these basic math problems please
Answer:
.
Step-by-step explanation:
a.) 72 ÷ 8 × 9 = 81 (we divide 72 by 8 first then multiply the result with 9)
b.) -72 ÷ 8 × 9 = -81 (it's same with a only differ by negative sign)
c.) 72 ÷ (-8) × 9 = -81 (dividing 72 by -8 will give us -9 and multiplying -9 by -9 will give the result of -81)
d.) 72 ÷ 8 × (-9) = -81 (divide 72 by 8 and it will be 9, mutliply it by -9 and again it will give -81)
e.) -72 ÷ 8 × (-9) = 81 (divide -72 by 8 and it will be -9 multiplying it by -9 will give a positive 81 since two negative signed numbers multiplied or divided gives positive result)
Answer:
A)81
B)-81
C)-81
D)-81
E)81
Step-by-step explanation:
ASAP HELP
please help with these six questions, use the graph i attached.
1. What is the amplitude of this function?
2. What is the period to the graph in problem 1?
3. What is the frequency of the function from problem 1?
4. What is the equation of the midline for the function from problem 1? (no spaces when typing equation)
5. What is the maximum value of the function from problem 1?
6. What is the minimum value of the function from problem 1?
Answer:
i) amplitude is 4/2 =2
ii) period of the graph = 3.14 ( radians), (or 180°)
iii) the frequency of the given function is f = 2Hz ( hertz).
iv) The midline for the function is y = -3.
v) The maximum value of the problem of the function is -1.
vi) the minimum value of the function is -5.
Step-by-step explanation:
i) the Peak to Peak is = -1 - (-5) = 4
therefore amplitude is 4/2 =2
ii) The period of the graph = 3.14
iii) one cycle is over 2π radians
one cycle of the given function is over π radians. Therefore the given
function will have 2 cycles over 2π radians. Therefore the frequency of the given function is f = 2 hertz.
iv) The midline for the function is y = -3.
v) The maximum value of the problem of the function is -1
vi) the minimum value of the function is -5.
___________ is the level of measurement where outcomes are based on some underlying continuum where it is possible to speak about how much more a higher performance is than a lower one:
Answer:
Interval level of measurement
Step-by-step explanation:
Interval level of measurement:
Interval level of measurement specifies the difference in two measurement on scale.Here, the difference between two values have meaning.Here, the negative value of measurement makes sense.The true zero does not exist.For example: Temperature.Thus,
Interval level of measurement is the level of measurement where outcomes are based on some underlying continuum where it is possible to speak about how much more a higher performance is than a lower one:
2 math questions. Please show your work if you can, I struggle with this, Thanks !!
20pts
Step-by-step explanation:
To find the solution, Tanisha can graph each side of the equation as its own function:
y₁ = log₃(5x)
y₂ = log₅(2x + 8)
The solution is where the two curves cross. From the graph, that happens at x ≈ 0.957.
desmos.com/calculator/lkukjhn3g2
Triangle FGH is translated using the rule (x,y) > (x+3,y-1). What are the coordinates of H ?
Answer: [tex]H'(4,-3)[/tex]
Step-by-step explanation:
For this exercise you must remember that the original figure (before a transformation) is called "Pre-Image" and the one obtained after the transformation is called "Image".
A Translation is defined as a transformation in which the figure is moved a fixed distance in a fixed direction. In this kind of transformatiosn the size and shape do not change and the figure is not flipped.
In this case you know that the Pre-Image is the Triangle FGH.
You can identify in the picture that its vertex H has these coordinates:
[tex]H(1,-2)[/tex]
Where:
[tex]x=1\\y=-2[/tex]
Since the rule is:
[tex](x,y)[/tex] → [tex](x+3,y-1)[/tex]
You can substitute the coordinates of H into the given rule in order to find the coordinates of H'. This is:
[tex]H'=(1+3,-2-1)=(4,-3)[/tex]
The coordinates of H after translation using the rule (x,y) > (x+3,y-1) are obtained by adding 3 to the x-coordinate and subtracting 1 from the y-coordinate of H's original position.
Explanation:To determine the coordinates of H after applying the translation rule (x,y) > (x+3,y-1), you have to add 3 to the x-coordinate and subtract 1 from the y-coordinate of point H's original position.
For example, if H originally has coordinates (a,b), then after the translation, the new coordinates of H will be (a+3, b-1).
The given translation rule does not change regardless of the element being translated, be it point or vector, as the rule is applied to each coordinate independently.
Therefore, if you know the original coordinates of point H, you just apply the rule directly to find the translated coordinates.
PLEASE HELP!!
Mario simplified the expression (4z^8)^-3 as shown.
(4z^8)^-3 = 4z^8 x (-3) = 4z^-24 = 4/z^24
Which statement explains Mario’s error?
He should have added the exponents instead of multiplying them.
He should have subtracted the exponents instead of multiplying them.
He should have applied the exponent –3 to 4, and not to z, to get 4^-3z^8 = 4^-3z^8 = z^8/64.
He should also have applied the exponent –3 to 4 to get 4^-3z^8 x (-3) = 4^-4 z^-24 = 1/64z^24.
Answer:
The answer to your question is the last choice
Step-by-step explanation:
[tex](4z^{8})^{-3}[/tex]
Process
1.- Use the exponent law "Power"
[tex]4^{-3} z^{(8)(-3)}[/tex]
2.- Simplify
[tex]4^{-3} z^{-24}[/tex]
3.- Use the exponent law "Negative exponent"
[tex]\frac{1}{4^{3} z^{24}}[/tex]
[tex]\frac{1}{64z^{24}}[/tex]
4.- Conclusion
He should have applied the exponent -3 to 4 to get [tex]\frac{1}{64z^{24}}[/tex]
Answer:
d
Step-by-step explanation:
Andre has been practicing his math facts. He can now complete 135 multiplication facts in 90 seconds. If Andre is answering questions at a constant rate, how many facts can he answer per second?
Andre can complete 1.5 facts in one second.
Step-by-step explanation:
Given,
Number of multiplication facts completed in 90 seconds = 135
Therefore;
90 seconds = 135 facts
Dividing both sides by 90 to fins the facts per second
[tex]\frac{90}{90}\ seconds=\frac{135}{90}\ facts\\\\1\ second = 1.5\ facts[/tex]
Andre can complete 1.5 facts in one second.
Keywords: unit rate, division
Learn more about unit rates at:
brainly.com/question/13063819brainly.com/question/13219835#LearnwithBrainly
Andre can answer 1.5 multiplication facts per second by dividing the total number of facts he completed (135) by the time it took (90 seconds).
Explanation:Andre has been answering multiplication facts at a consistent pace. To find out how many facts he can answer per second, we need to divide the total number of facts he answered by the total number of seconds it took him to answer them.
Andre answered 135 multiplication facts in 90 seconds.
To calculate the rate per second, the formula is:
Division of total facts by total seconds: 135 facts ÷ 90 seconds = 1.5 facts per second.Therefore, Andre can answer 1.5 facts per second.
PLEASE HELP!!! PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!! I NEED TO FINISH THESE QUESTIONS BEFORE MIDNIGHT TONIGHT.
Find CD.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
CD =
Answer:
[tex]CD = 7.8[/tex]
Step-by-step explanation:
Given:
Δ DBC is a right angled triangle.
[tex]\angle B = 90\°\\\\\angle C = 59\°[/tex]
BC = 4
We need to find the value of CD
Solution:
Now we know that:
[tex]cos\ \theta = \frac{adjacent \ side}{hypotenuse}[/tex]
So we can say that;
[tex]Cos \angle C =\frac{BC}{CD}[/tex]
Substituting the given values we get;
[tex]Cos\ 59 = \frac{4}{CD}\\\\\\CD = \frac{4}{Cos\ 59} = 7.766[/tex]
Rounding to nearest tenth we get;
[tex]CD = 7.8[/tex]
Hence the Value of CD is 7.8.
The ages of three siblings Jason John and Jackson totals 21 years. Jason is one year older than John. Jackson is three times as old as John. How old is John?
Answer:Jason is 5 years old.
John is 4 years old.
Jackson is 12 years old.
Step-by-step explanation:
Let x represent the age of Jason.
Let y represent the age of John.
Let z represent the age of Jackson.
The ages of three siblings Jason John and Jackson totals 21 years. It means that
x + y + z = 21 - - - - - - - - - - -1
Jason is one year older than John. It means that
x = y + 1
Jackson is three times as old as John. It means that
z = 3y
Substituting x = y + 1 and z = 3y into equation 1, it becomes
y + 1 + y + 3y = 21
5y = 21 - 1 = 20
y = 20/5 = 4
x = y + 1 = 4 + 1
x = 5
z = 3y = 3 × 4
z = 12