To build a scale model, the student's school height is first converted to centimeters using the scale factor (50.4 cm), then divided by the length of a toothpick and a cotton swab respectively to determine how many of each would be needed to reach the scaled height. The model will be 8 toothpicks tall and approximately 7 cotton swabs tall.
To solve the problem of building a scale model of the student's school, we need to apply the scale factor provided and the measurements of the materials at hand. The school is 30 feet tall, and the scale is 1 ft:1.68 cm.
To calculate the height of the model in toothpicks, we'll convert the height of the school from feet to centimeters, and then divide by the length of a toothpick:
Multiply the actual height by the scale factor: 30 ft × 1.68 cm/ft = 50.4 cm.Divide the scaled height by the length of a toothpick: 50.4 cm ÷ 6.3 cm/toothpick = 8 toothpicks. Therefore, the model will be 8 toothpicks tall.For the model in cotton swabs, we'll also convert the height to centimeters and then divide by the length of a cotton swab:
Multiply the actual height by the scale factor: 30 ft × 1.68 cm/ft = 50.4 cm.Divide the scaled height by the length of a cotton swab: 50.4 cm ÷ 7.2 cm/cotton swab = 7 cotton swabs. After rounding, the model will be approximately 7 cotton swabs tall.Complete Question is :
"You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.68 cm. If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be? The model will be toothpicks tall. Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.2 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number. The model will be approximately cotton swabs tall."
What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.
x = i and x = 5
x=t i and x = = 15
x=+ -1 and x = 1 -5
X= + -1 and x = 1 - 5
Answer:
x = i and x = i[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Given
[tex]x^{4}[/tex] + 6x² + 5 = 0
Using the substitution u = x², then
u² + 6u + 5 = 0 ← in standard form
(u + 1)(u + 5) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 1 = 0 ⇒ u = - 1
u + 5 = 0 ⇒ u = - 5
Convert solutions back into terms of x
x² = - 1 ⇒ x = [tex]\sqrt{-1}[/tex] = i
x² = - 5 ⇒ x = [tex]\sqrt{-5}[/tex] = i[tex]\sqrt{5}[/tex]
Please help right away
Answer:
D) 5985
Step-by-step explanation:
Total area: 150×100 = 15000
Area for stars: 6×6 = 36
Total area - area for stars = area for fans
15000-36= 14964
14964ft² for fans, each takes up 2.5 ft²
14964 ÷2.5 = 5985.6 fans
Since we can't have 0.6 of a person, we round down to 5985 fans
Answer:
5,985 fans
Step-by-step explanation:
First you will need to get the floor area of the store
The dimensions are:
150' by 100'
This is 150 ft by 100 ft
Area would be:
Side x side (Assuming that the floor area is a quadrilateral)
150 ft x 100 ft = 15000 ft²
Next we solve for the area of the stars only:
6' by 6'
Side x side
6 ft x 6 ft = 36 ft²
So here we subtract the stars only area from the total floor area:
15,000 ft² - 36 ft² = 14,964 ft²
This is the floor area that the fans can occupy.
Next since the fire marshal said 1 person must occupy an area no less than 2.5ft², we divide the floor area for fans by the requirement.
14,964 ft² = 5,985.6 fans
2.5ft²
Since we cannot have a decimal for people, we need to round it down. If it goes beyond 5,985.6 that means we do not meet the minimum requirement of 2.5 ft² per person. So we need to round it down, to the nearest whole number, the answer would be:
5,985 fans.
did I do this correctly?
Answer:
No, The answer should be 240
Step-by-step explanation:
The first step to finding the Surface Area was done well and was right but you got confused when trying to add the area of each shapeThere is 3 Rectangles and 2 Traingles. Let's start with the area of the triangles. 1/2bh is the formula for finding area of Traingles. 1/2(4)(6) = 12. We have two Traingles so that would be 24. Now we have three rectangles with different lengths we need to calculate. Rectangle 1 = 12 * 8 = 96Rectangle 2 = 12 * 6 = 72 Rectangle 3 = 12* 4 = 4824+96+72+48 = 240. So, the surface area of the rectangular prisim is 240Brand Y Cola sponsors a survey of 15,559 residents of Texas to determine which brand of cola they prefer. Forty percent say they prefer Brand X, and 60 percent say they prefer Brand Y. Which of the following is the population sample?
Answer:
B. the 15,559 residents
Step-by-step explanation:
I just took the final exam
Brainist and 40 pt please help
And show your work
Answer:
n > 2
Step-by-step explanation:
-10 − -3n > -4
-10 + 3n > -4
3n > 6
n > 2
Check our answer: if n = 3:
-10 − -3(3)
-10 − -9
-10 + 9
-1
-1 > -4
-10 - (-3n) > -4 ---> -10 + 3n > -4
^^^^ -3n became positive because a negative times a negative gives a positive
Step 1: Combine like terms
normal numbers go with normal numbers. This would be -10 and -4. To get -10 to the right side of the inequality you must add 10 to both sides
(-10 + 10) + 3n > (-4 + 10)
(0) + 3n > 6
3n > 6
Step 2: Isolate n by dividing 3 to both sides of the inequality
[tex]\frac{3n}{3} > \frac{6}{3}[/tex]
n > 2
Hope this helped!
the three steps below were used to find the value of the expression [(-10+2)-1]+(2+3)
[(-10+2)-1]+(2+3) is equal to -4.
What is an expression in Mathematics?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.
Given
[(-10+2)-1]+(2+3)
Using BODMAS
= [-8 - 1] + 5
= -9 + 5
=-4
Therefore, [(-10+2)-1]+(2+3) is equal to -4.
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Final answer:
The value of the expression [(-10+2)-1]+(2+3) is found by following the order of operations; handle the parentheses first, then sum the results, which leads to a final answer of -4.
Explanation:
Step-by-Step Solution to the Expression
To find the value of the expression [(-10+2)-1]+(2+3), you follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, solve inside the parentheses: (-10+2) gives you -8.
Next, (-8-1) simplifies to -9, so now you have [-9].
Then, you solve the addition within the other set of parentheses: (2+3) which equals 5.
Finally, you add the results of the two sets of parentheses: -9 + 5.
Following addition rules for numbers with opposite signs, you subtract the smaller number from the larger one and keep the sign of the larger number, which in this case is negative. Thus, -9 + 5 equals -4.
Therefore, the value of the expression is -4.
Fill in the blank to make the fractions equivalent.
8/12 = _/3
using a hose, katelyn is spraying water into the air and initial velocities of 48 feet per second. the function h(t)=-16t^2+48t+4 represents the path of the water from the hose. what is the maximum height of the water?
36 feet
40 feet
44 feet
48 feet
Check the picture below.
so then, the highest point will be at the y-coordinate of its vertex.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+48}t\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left( \qquad ,~~4-\cfrac{48^2}{4(-16)} \right)\implies \left( \qquad ,~~4+\cfrac{2304}{64} \right)\implies (\qquad ,~4+36) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\qquad ,~~\stackrel{\stackrel{\textit{how high}}{\textit{it went}}}{40})~\hfill[/tex]
Match each description with its symbolic representation.
1. P(A)
2. PAB)
3. P(AUB)
The probability that event A occurs
given the fact that event B occurs
The probability that either event A
or event B occurs
The probability that both events A
and B do not occur together, but either
may occur by itself
The probability that neither event A
or event B occurs
The probability that event A occurs
The probability that both event A
and event B occur
4. 1 - P(ANB)
5. 1- P(AUB)
6. P(AIB)
NEYT QUESTION
ASY OR WIP
TURN IT IN
Answer:
i) P(A) ; The probability that event A occurs
ii) P(AB) ; The probability that both event A and event B occur
iii) P(AUB) ; The probability that either event A or event B occurs
iv) 1 - P(ANB) ; The probability that both events A and B do not occur together, but either may occur by itself
v) 1- P(AUB) ; The probability that neither event A or event B occurs
vi) P(AIB) ; The probability that event A occurs given the fact that event B occurs
Step-by-step explanation:
i)
P(A) simply represents the probability that an event A will occur. This event could be passing an examination, having snow in summer, arriving to work on time and so forth.
ii)
P(AB) is simply the probability that both event A and event B do occur. This is usually given by the product of the individual probabilities. Event A could be rolling a 6 in one throw of a fair die while B could be the event that a fair coin lands heads in a single toss.
iii)
P(AUB) refers to the probability that either event A or event B occurs. This is read out as the probability of A union B. This is usually given by the sum of the individual probabilities.
iv)
1 - P(ANB) is the probability that both events A and B do not occur together, but either may occur by itself. P(ANB) is the probability that both events A and B occur together. This is read out as the probability of A intersection B. Therefore implying that 1 - P(ANB) is simply the probability that either event A or B occurs but A and B can not occur together.
v)
1- P(AUB) refers to the probability that neither event A or event B occurs. Earlier we defined P(AUB) as the probability that either event A or event B occurs. 1- P(AUB) simply the complement of P(AUB).
vi)
P(AIB) refers to the probability that event A occurs given the fact that event B occurs. This is a conditional probability event which evaluates the likelihood of an event A occurring given that an associated event B has already occurred
Need help with this question any help would be very appreciated
Answer:
Between A and B : Decreasing
Between B and C : Increasing
Between C and D : Decreasing
Between D and E : Constant
Step-by-step explanation:
If graph goes downward between two points then it indicates function is decreasing.
If graph goes upward between two points then it indicates function is increasing.
If graph goes parallel to the x-axis between two points then it indicates function is constant.
Then final answer is given by:
Between A and B : Decreasing
Between B and C : Increasing
Between C and D : Decreasing
Between D and E : Constant
A sandwich shop has 18 tables. Each table seats up to 4 people. To find the greatest number of people that can be seated, you can solve p4 ≤ 18. Which step is the best way to solve the inequality?
Answer:
I did this test. The answer to this question is c.multiply each side by 4
Step-by-step explanation:
PLEASE ANSWER ASAP What is the value of x in the equation 1.8-3.7x=-4.2+0.3?
Answer:
X=57/37 , X=1.540
What are the outcomes in a or b?
Answer:
its c
Step-by-step explanation:
Answer b:
Step-by-step explanation:
If x = 2 calculate the value of x squared- x
Simplify (6x^2-34x+20)/((2x^2+3)(x-5))
2[-2 + 3x]\3 + 2x² is the simplification.
the function f(x)= 3x squared+12x+11 can be written in vertex form as A. f(x)=(3x+6) squared-25 B. f(x)=3(x+6) squared-25 C. f(x)= 3(x+2) squared-1 D. f(x)= 3(x+2) squared+7) explain and show your work and what is vertex form
Answer:
[tex]\boxed{\text{C. }{f(x) =3(x + 2)^{2} - 1}}[/tex]
Step-by-step explanation:
The vertex form of a quadratic function
ƒ(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
You convert ƒ(x) = 3x² + 12x + 11 to the vertex form by completing the square.
Step 1. Move the constant term to the other side of the equation
y - 11 =3x² + 12x
Step 2. Factor out the leading coefficient
y - 11 =3(x² + 4x)
Step 3. Complete the square on the right-hand side
Take half the coefficient of x, square it, and add it to each side of the equation.
4/2 = 2; 2² = 4
y – 11 + 12 =3(x² + 4x + 4)
Note that when you completed the square by adding 4 inside the parentheses, you were adding 3×4 to the right-hand side, so you had to add 12 to the left-hand side.
Step 4. Simplify and write the right-hand side as a perfect square
y + 1 = 3(x + 2)²
Step 5. Isolate the y term
Subtract 1 from each side
y = 3(x + 2)² -1
[tex]\text{The vertex form of the equation is }\boxed{\mathbf{f(x) =3(x + 2)^{2} - 1}}[/tex]
If you compare this equation with the general vertex form and with the graph, you will find that h = -2 and k = -1, so the vertex is at (-2, -1).
The quadratic equation f(x) = 3x^2 + 12x + 11 can be rewritten in vertex form as C. f(x) = 3(x + 2)^2 - 1 after completing the square.
Explanation:The function f(x) = 3x2 + 12x + 11 can be rewritten in vertex form, which is y = a(x - h)2 + k, where (h, k) represents the vertex of the parabola. To convert the given quadratic to vertex form, we need to complete the square:
Group the x-terms together: f(x) = 3(x2 + 4x) + 11Complete the square: f(x) = 3(x2 + 4x + 4 - 4) + 11 = 3((x + 2)2 - 4) + 11Simplify: f(x) = 3(x + 2)2 - 12 + 11 = 3(x + 2)2 - 1So, the correct vertex form of the equation is C. f(x) = 3(x + 2)2 - 1.
during football practice a football player kicks a football. the height h in feet of the ball t seconds after it is kickedcan be modeled by thr function h=-4(4t-11). how long is the football in the air?
The football, kicked by a football player during a practice, is in the air for approximately 3.79 seconds based on the model h = -4(4t - 11)^2.
Explanation:The question asks for the duration that the football is in the air. This problem involves solving a quadratic function to determine the time when the height of the ball is zero, i.e., when it hits the ground again. The mentioned equation and given information form a quadratic equation.
The equation h = -4(4t - 11)^2 models the height of the football at any given time. The football is on the ground when h = 0. If we substitute h = 0, the equation becomes -4(4t - 11)² = 0. Using the quadratic formula, we find two solutions t = 0.54 s and t = 3.79 s.
As we are looking for the total time that the football is in the air, we are interested in when it falls back to the ground which corresponds to the larger solution. Therefore, the football is in the air for approximately 3.79 seconds.
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The football is in the air for 2.75 seconds.
Explanation:The given function h = -4(4t-11) models the height h of the ball t seconds after it is kicked. To find how long the football is in the air, we need to find the time when the ball reaches the ground. This occurs when the height h is equal to 0. So, we can set the equation -4(4t-11) = 0 and solve for t.
-4(4t-11) = 0
4t-11 = 0
4t = 11
t = 11/4
Hence, the football is in the air for 11/4 seconds or 2.75 seconds.
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If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is
Answer:
As a fraction: [tex]y=\frac{56}{5}[/tex]
As a decimal: [tex]y=11.2[/tex]
As an ordered pair: [tex](0,\frac{56}{5} )[/tex] or [tex](0,11.2)[/tex]
Step-by-step explanation:
First we are using the slope formula to find the equation of our line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where
[tex]m[/tex] is the slope of the line
[tex](x_1,y_1)[/tex] are the coordinates of the first point
[tex](x_2,y_2)[/tex] are the coordinates of the second point
our first point is (8, 0) and our second point is (3, 7), so [tex]x_1=8[/tex], [tex]y_1=0[/tex], [tex]x_2=3[/tex], and [tex]y_2=7[/tex].
Replacing values:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-0}{3-8}[/tex]
[tex]m=\frac{7}{-5}[/tex]
[tex]m=-\frac{7}{5}[/tex]
Now, to complete the equation of our line (and find its y-intercept), we are using the point slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
Replacing values:
[tex]y-0=-\frac{7}{5} (x-8)[/tex]
[tex]y=-\frac{7}{5} x+\frac{56}{5}[/tex]
Now, in a line of the form [tex]y=mx+b[/tex], [tex]b[/tex] is the way intercept. We can infer form our line that [tex]b=\frac{56}{5}[/tex], so the y-intercept of the line joining the points (8, 0) and (3, 7) is [tex]\frac{56}{5}[/tex].
The EU has challenged the U.S."s position in the global economy. True or False
Answer:
False
Step-by-step explanation:
EU and the US are very good friends and they often trade with them.
Answer:
The answer to your question is True
Step-by-step explanation: Because The EU is largely viewed as a cornerstone of European stability and prosperity. For much of the last decade, however, many EU countries have faced considerable economic difficulties.
Hope this helps :)
And please mark my answer as the brainliest
Write an equation that represents a vertical translation 7 units down of the graph of g(x) = 21.
h(x) -
Answer:
h(x) = 14Step-by-step explanation:
f(x) + n - translation n units up
f(x) - n - translation n units down
f(x + n) - translation n units to the left
f(x - n) - translation n units to the right
===========================================
g(x) = 21
translation 7 units down: g(x) - 7 = 21 - 7 = 14
Moving a graph or function vertically down is as simple as subtracting the number of units you wish to move from the original function. The function g(x) = 21 moved 7 units down resulting in h(x) = 14.
Explanation:A vertical translation in a graph is a shift in the graph either up or down along the y-axis. In the case of the function g(x) = 21, which is a horizontal line at y = 21, a vertical translation 7 units down would yield the new function h(x) = 21 - 7 = 14. Therefore, the equation that represents this translation is h(x) = 14.
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Can anybody please help me ?
1 The average salary for a professional baseball player in the United States can be approximated by = 283(1.2)^t where t=0 represents the year 1984. Using this approximation, find the ratio of an average salary in 1988 to the average salary in 1994.
2 Find and correct the error(s) in the problem below. Explain your correction(s).
x^-9/x^-3=x^-9-3
=x^-12
=1/x^-12
Here the answer is in this picture
Answer:
1. Ratio is 1 : 3
Step-by-step explanation:
1. The average salary for a professional baseball player in the United States can be approximated by = [tex]283(1.2)^{t}[/tex]
Where t = 0 represents the year 1984.
Salary in year 1988 = [tex]283(1.2)^{4}[/tex] [t = 4 years]
Salary in year 1994 = [tex]283(1.2)^{10}[/tex] [t = 10 years]
Ratio of the average salary in 1988 to the average salary in 1994 = [tex]\frac{283(1.2)^{4}}{283(1.2)^{10}}=\frac{(1.2)^{4}}{(1.2)^{10}}[/tex]
= [tex]\frac{1}{(1.2)^{10-4}}=\frac{1}{(1.2)^{6}}[/tex]
= [tex]\frac{1}{3}[/tex]
2. Corrected form
[tex]\frac{x^{-9} }{x^{-3}}[/tex]
= [tex]x^{-9+3}[/tex][since [tex]\frac{a^{1}}{a^{1}}=a^{1-1}=a^{0}=1[/tex]]
= [tex]x^{-6}[/tex]
= [tex]\frac{1}{x^{6}}[/tex] [ since [tex]\frac{1}{a^{1}}=a^{-1}[/tex] ]
Now we can compare the corrections and errors in the highlighted form.
Expression needs correction
[tex]\frac{x^{-9} }{x^{-3}}[/tex]
= [tex]x^{-9-3}[/tex]
= [tex]x^{-12}[/tex]
= [tex]\frac{1}{x^{-12}}[/tex]
Solve the inequality. Graph the solution set. 26 +6b>2(3b+4)
Answer:
True for all b
Interval notation; (-∞, ∞)
Step-by-step explanation:
We have been given the following inequality;
26+6b>2(3b+4)
The first step is to open the brackets on the right hand side;
26+6b>6b+8
26-8>6b-6b
18>0
Since 18 is actually greater than 0, the solution set to the inequality is;
True for all b.
Subtract. negative 10.0 minus left parenthesis negative 2.3 right parenthesis
If you mean -10.0 - (-2.3) then the answer is -7.7
Final answer:
To subtract -10.0 - (-2.3), you change the subtraction of the negative number to addition and calculate -10.0 + 2.3, resulting in -7.7.
Explanation:
Subtracting a negative number from another negative number is equivalent to adding the absolute value of the number being subtracted. To solve the given problem, we can visualize it as negative 10.0 plus 2.3.
The subtraction of two negative numbers can be transformed into an addition problem by remembering that subtracting a negative is the same as adding a positive. Here is how you would calculate it step-by-step:
Start with the first number: -10.0.
Change the subtraction to addition because subtracting a negative is like adding a positive.
Add the absolute value of the second number: +2.3.
Combine both numbers: -10.0 + 2.3 = -7.7.
So, negative 10.0 minus (negative 2.3) equals -7.7.
I Need this answered asap thanks for helping
Answer:
y = 3 or y = 7Step-by-step explanation:
[tex]\bold{METHOD\ 1}\\(y-3)^2=4y-12\\\\(y-3)^2=4(y-3)\\\\(y-3)(y-3)=4(y-3)\iff y-3=0\ \vee\ y-3=4\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}\\\\y-3=4\qquad\text{add 3 to both sides}\\\boxed{y=7}[/tex]
[tex]\bold{METHOD\ 2}\\\\(y-3)^2=4y-12\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\y^2-2(y)(3)+3^2=4y-12\\\\y^2-6y+9=4y-12\qquad\text{subtract}\ 4y\ \text{from both sides}\\\\y^2-10y+9=-12\qquad\text{add 12 to both sides}\\\\y^2-10y+21=0\\\\y^2-3y-7y+21=0\\\\y(y-3)-7(y-3)=0\\\\(y-3)(y-7)=0\iff y-3=0\ \vee\ y-7=0\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}\\\\y-7=0\qquad\text{add 7 to both sides}\\\boxed{y=7}[/tex]
How can we use theorems about the angles formed by transversals to help ensure that lines are parallel in the design and construction of real-world structures?
Answer:
We can use this knowledge in planning of cities
Step-by-step explanation:
The transversal is a line that intersects two or more parallel lines.Angles with similar characteristics are formed when this occurs.
In city planning, streets can be designed to resemble parallel lines with roads that do not meet.However, other roads can be constructed to allow people on the other street to cross to neighboring streets.Such roads allowing this access can be viewed as transversal.
The areas where street roads meet the transversal roads have similar angle characteristics thus could be used for CCTV cameras for surveillance and traffic lights positioning.
Find the discount rate
Retail Price: $27.99
Discount: $12
Sale Price: $15.99
(Please show your work)
we'd do the same as before on this one as well.
if we take 27.99 to be the 100%, what is 12 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 27.99&100\\ 12&x \end{array}\implies \cfrac{27.99}{12}=\cfrac{100}{x}\implies 27.99x=1200 \\\\\\ x=\cfrac{1200}{27.99}\implies x\approx 42.87[/tex]
The discount rate can be determined by dividing the discount by the retail price, then multiplying by 100 to get the percentage. In this instance, the discount rate calculates to be approximately 42.87%.
Explanation:To find the discount rate, you must first understand that it is the difference between the retail price and the sale price, divided by the retail price, and then multiplied by 100 to turn it into a percentage.
In this case, let's use the numbers from the problem. The retail price is $27.99 and the discount is $12, leaving a sale price of $15.99. We already know the discount is $12, so to find the rate we divide $12 (the discount) by $27.99 (the original price), and then multiply by 100.
Doing the calculation, ($12/$27.99) * 100 = approx. 42.87%. So the discount rate is approximately 42.87%.
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A triangle has an area of 64 yd and a base of 8 what is the height of the triangle?
[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=64\\ b=8 \end{cases}\implies 64=\cfrac{1}{2}(8)h\implies 64=4h \\\\\\ \cfrac{64}{4}=h\implies 16=h[/tex]
Which is an equivalent equation solved fort?
The equation f = v + at represents the final velocity of an
object, f, with an initial velocity, V, and an acceleration rate,
a, over time, t
o t=
t=alf-v)
t = v(f-a)
Answer:
t = (f - v)/a
Step-by-step explanation:
We have been given that;
The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t.
The question requires us to solve for t;
The first step is to subtract v on both sides of the equation,
f - v = v + at - v
f - v = at
The next step is to divide both sides by a,
(f - v)/a = t
which is our required equation solved for t.
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given.
Find its area and round to the nearest tenth.
Please Help Me!!
Answer:
26.04cm^2
Step-by-step explanation:
28 divided by 20 is 1.4. 1.4 times the area will give you the area of the other figure. 1.4 x 18.6 = 26.04
use scale faction to solve and you get
36.5cm^2!
On a graphing calculator, you can use the function normalcdf(lower bound, upper bound, μ, σ) to find the area under a normal curve for values of x between a specified lower bound and a specified upper bound. You can use −1E99 as the lower bound to represent negative infinity and 1E99 as the upper bound to represent positive infinity. Suppose that cans of lemonade mix have amounts of lemonade mix that are normally distributed with a mean of 350 grams and a standard deviation of 4 grams. What percent of cans have less than 362 grams of lemonade mix?
__% of cans have less than 362 grams of lemonade mix.
Answer:
99.87% of cans have less than 362 grams of lemonade mix
Step-by-step explanation:
Let the the random variable X denote the amounts of lemonade mix in cans of lemonade mix . The X is normally distributed with a mean of 350 and a standard deviation of 4. We are required to determine the percent of cans that have less than 362 grams of lemonade mix;
We first determine the probability that the amounts of lemonade mix in a can is less than 362 grams;
Pr(X<362)
We calculate the z-score by standardizing the random variable X;
Pr(X<362) = [tex]Pr(Z<\frac{362-350}{4})=Pr(Z<3)[/tex]
This probability is equivalent to the area to the left of 3 in a standard normal curve. From the standard normal tables;
Pr(Z<3) = 0.9987
Therefore, 99.87% of cans have less than 362 grams of lemonade mix