Answer:
D. Up
Step-by-step explanation:
When a parabola has the form [tex]y=ax^2+bx+c[/tex] , It is vertical (opens up or down).
Because the variable "x" is squared.
If "a" is positive, then the parabola opens up, but if it is negative, then the parabola opens down.
In this case you have the quadratic function:
[tex]f(x) = 2x^2+5x-4[/tex]
Which can be rewritten as:
[tex]y = 2x^2+5x-4[/tex]
Therefore, it is vertical, because it has the form: [tex]y=ax^2+bx+c[/tex]
You can observe that the value of "a" is:
[tex]a=2[/tex]
Then, since "a" is positive, the parabola opens up.
Which of the following illustrates the truth value of the given conditional statement? If 3 + 2 = 5, then 5 + 5 = 10. T F → F T T → T F T → T F F → F
Answer:
T T → T
Step-by-step explanation:
A conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 3 + 2 = 5 which is true and 5 + 5 = 10 which is also true.
Which of the following is not an example of exponential growth or decay? A. a t-shirt shrinks by 2% after each wash B. a one time bonus of 10% of a worker’s annual salary C. a yearly pay increase of 3% each year D. a savings account growing by 3% each year
Final answer:
Option B, a one-time bonus of 10% of a worker’s annual salary, is not an example of exponential growth or decay because it does not involve a percentage change being applied repeatedly over time to a changing base amount.
Explanation:
The question asked is: Which of the following is not an example of exponential growth or decay? The options are: A. a t-shirt shrinks by 2% after each wash, B. a one time bonus of 10% of a worker’s annual salary, C. a yearly pay increase of 3% each year, D. a savings account growing by 3% each year. To answer this, we must recognize that exponential growth or decay refers to processes that grow or decrease at a rate proportional to their current size. This means the amount of increase or decrease changes over time, as it is a percentage of an ever-changing base amount.
Options A, C, and D all describe situations where the quantity changes by a fixed percentage over time, indicative of exponential growth (or decay, in the case of shrinking). Option A discusses a t-shirt shrinking by 2% after each wash, meaning each time it shrinks, it does so based on its current size, which is a characteristic of exponential decay. Option C talks about a yearly pay increase of 3% each year, and Option D describes a savings account growing by 3% each year; both are examples of exponential growth. Therefore, the answer is Option B, a one-time bonus of 10% of a worker’s annual salary, as it does not describe a situation where the growth rate is applied over time to an ever-changing base amount.
The given tables each show the number of stories completed in the construction of four different high-rise buildings and the number of days spent working on the building. Which table best represents a linear relationship? '
A. Number of Days 140 300 520 740 960 Number of Stories 4 8 12 16 20
B. Number of Days 120 240 360 480 600 Number of Stories 5 10 15 20 25
C. Number of Days 30 60 120 240 480 Number of Stories 2 4 6 8 10
D. Number of Days 90 225 400 680 960 Number of Stories 3 6 9 12 15
Answer:
The correct answer option is B. Number of Days 120 240 360 480 600 Number of Stories 5 10 15 20 25.
Step-by-step explanation:
We are given some tables showing the number of stories completed in the construction of four different high-rise buildings and the number of days spent working on the building.
We are to determine whether which table represents a linear relationship.
Table B represents a linear relationship since its ratio of number of days to number of stories completed is constant.
Number of Days 120 240 360 480 600
Number of Stories 5 10 15 20 25
Ratio 24 24 24 24 24
Depending on the day of the week, a border guard searches every nth person coming across the border. Each Tuesday every 7th person is checked. What is the name of this method of sampling?
Convenience Sampling
Systematic Random Sampling
Stratified Random Sampling
Simple Random Sampling
the answer is "Systematic Random Sampling"
I NEED THE ANSWER ASAP
Jasmin and Jarvis are going to the donut shop. They have two options, donuts or donut holes and two toppings chocolate or sprinkles. Create a tree diagram to represent the sample space.
So first do the diagram (vent) and but two and two donuts until a odd number pops I think the answer is 5.
The volume of the cylinder is 5275 ft and the height is 23 find the diameter please explain this is for school tomorrow
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} V=5275\\ h=23 \end{cases}\implies 5275=\pi r^2(23)\implies \cfrac{5275}{23\pi }=r^2 \\\\\\ \sqrt{\cfrac{5275}{23\pi }}=r\implies 15.144\approx r~\hspace{10em}\stackrel{diameter=2r}{d\approx 30.288}[/tex]
The hypotenuse of a right triangle is 3cm and one of the legs is 1cm. What is the length of the other leg?
A. 4cm
B. Square root 10cm
C. 2cm
D. 2 Square root 2cm
Check the picture below.
Kai correctly used the different laws of logarithms to rewrite log27 - log(3/5) -log 5 as one logarithm.
His work is shown here
Step one: Log27-(log3- log5) -log 5
Step two: log (3^3) -log 3+ log 5- log 5
Step three: log (3^3) - log3
Step 4: 3 log3- log 3
Step 5: 2 log 3
Step 6: log (3^2)
Step 7: log 9
In which step(s) did kai apply the difference law for logarithms
A- step 3
B- step 5
C- step 4
D- step 1
Answer:
A
Step-by-step explanation:
Final answer:
In step 3 of Kai's calculations, he applied the difference law for logarithms.
Explanation:
In step 1, Kai applied the difference law for logarithms by subtracting the logarithms of 3 and 5 from the logarithm of 27.
In step 3, Kai further simplified by using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. In this case, he applied this property to rewrite 3^3 as (3^2).
Therefore, the correct answer is Step 3.
Suppose you had to decide between an apartment that costs $800/month for a month-to-month contract, or $650/month for an annual contract. The annual contract includes a 2-month early termination penalty if you leave before 12 months. Now, suppose you chose the annual contract. If you leave after 8 months, which option would be the most cost effective?
Answer:
the second one would be more effective because $800*12 will cost a lot more than $650+2 months penalty if u leave
Estimate the line of best fit using two points on the line. (10, 32) (20, 62)
A. y = 10x
B. y = 3x + 2
C. y = 10x + 10
D. y = 3x + 20
B. 3x+2 is the correct answer
Answer: The correct option is
(B) [tex]y=3x+2.[/tex]
Step-by-step explanation: We are given to estimate the line of best fit using the following two points on the line.
(10, 32) and (20, 62).
We know that
the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the given line will be
[tex]m=\dfrac{62-32}{20-0}=\dfrac{30}{10}=3.[/tex]
Since the line passes through the point (10, 32), so its equation is given by
[tex]y-32=m(x-10)\\\\\Rightarrow y-32=3(x-10)\\\\\Rightarrow y=3x+30+32\\\\\Rightarrow y=3x+2.[/tex]
Thus, the required equation of the line of best fit is [tex]y=3x+2.[/tex]
Option (B) is CORRECT.
1 litre is approximately 1.75 pints, 1 gallon = 8 pints, calculate the approcimate number of gallons that are equal to 48000cm3
Answer:
[tex]10.5\ gal[/tex]
Step-by-step explanation:
we know that
[tex]1,000\ cm^{3} =1\ l[/tex]
[tex]1\ l=1.75\ pints[/tex]
[tex]1\ gal=8\ pints[/tex]
we have
[tex]48,000\ cm^{3}[/tex]
step 1
Convert to liters
[tex]48,000\ cm^{3}=48,000/1,000=48\ l[/tex]
step 2
Convert to pints
[tex]48\ l=48*1.75=84\ pints[/tex]
step 3
Convert to gallons
[tex]84\ pints=84/8=10.5\ gal[/tex]
The approximate number of gallons that are equal to 48000cm3 is 12.67 gallons.
1 liter is approximately 1.75 pints, 1 gallon = 8 pints
To convert 48000 cm³ to gallons, first recognize that 1 liter is 1000 cm³.
Therefore, 48000 cm³ is 48 liters.
Next, knowing that 1 gallon is approximately 3.79 liters, divide 48 by 3.79 to get approximately 12.67 gallons.
plz help I'm lost!!!!!
Answer:
D.
Step-by-step explanation:
A linear function is one that has a constant rate of change.
On table D, we can see that it has a constant rate of +2 as every time x increases by 1, y increases by 2.
Answer:
D
Explanation:
Because linear function is having the same difference or in another way it’s having the same rate of change.
Good luck,!~s
A ball is shot into the air using a brand new super-high-tech robotic arm to help baseball players practice catch fly balls.
The ball has an initial upward velocity of 64 feet per second. The height, h, of the ball after t seconds is given by the
equation:
Answer:
69 feet
Step-by-step explanation:
we have
[tex]h(t)=-16t^{2}+64t+5[/tex]
where
h(t) is the height of the ball
t is the time in seconds
we know that the given equation is a vertical parabola open downward
The vertex is the maximum
so
the y-coordinate of the vertex represent the maximum height of the ball
Convert the quadratic equation into vertex form
The equation in vertex form is equal to
[tex]y=(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
[tex]h(t)=-16t^{2}+64t+5[/tex]
[tex]h(t)-5=-16t^{2}+64t[/tex]
[tex]h(t)-5=-16(t^{2}-4t)[/tex]
[tex]h(t)-5-64=-16(t^{2}-4t+4)[/tex]
[tex]h(t)-69=-16(t^{2}-4t+4)[/tex]
[tex]h(t)-69=-16(t-2)^{2}[/tex]
[tex]h(t)=-16(t-2)^{2}+69[/tex]
the vertex is the point (2,69)
therefore
The maximum height is 69 ft
Please help me!
Q) Two rectangles have the same width. One is 12 units long and the other is 8 units long. The area of the first rectangle is 320 square units more than the area of the second rectangle. Find the width of each rectangle.
Answer:
80
Step-by-step explanation:
A = Area of First Rectangle
B = Area of Second Rectangle
w = Width
12(w)=320+B (1st Equation)
8(w) = B (2nd Equation)
w=B/8 (Plug this value of w into the first equation)
12B/8 = 320 +B (you get this)
12B= 2560 + 8B (Simplify)
4B = 2560
B =640 plug this value into the 2nd equation
8(w) = 640
w = 80
To Test This
12x80 = 960
8x80 = 640
960 - 640 = 320 Therefore the answer is correct the width is 80
At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys. r + f ? 16 4r + 2f ? 40 What is the maximum number of ride tickets she can buy? 4 6 10 12
Answer:
4
Step-by-step explanation:
Here let the number of ride tickets be r, and the number of food tickets be f.
Hence
[tex]r+f\ge16\\4r+2f\le40[/tex]
We first plot the two inequalities on graph as shown in attachment. From the graph we see that the two in-equation meet at (4,12)
Hence we can see that the maximum value of r is 4
Answer:
4
Step-by-step explanation: the maximum number of ride tickets she can buy is 4. so option a is correct
Check my answer?
The law of cosines reduces to the Pythagorean Theorem when the triangle is right.
True or False
I select False
Answer: you have the correct answer hope this helped please mark me the brainlest answer have a good day mate
A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?
Answer:
The answer is 10
Step-by-step explanation:
The value of f(5) will be 10 for the given sequence.
What is Sequence?A grouping of two or more items in a logical sequence. the sequential arrangement of two or more items. The sequence is a term used to describe chronological order. You should be familiar with the following four primary categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. a collection of two or more elements arranged logically. the placement of two or more elements in a particular order. The word "sequence" refers to chronological order. Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four main types of sequences that you should be aware of.
Given, A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18.
for n = 1
f(2) = f(1) - 2 = 18 -2 = 16
for n = 2
f(3) = f(2) - 2 = 16 - 2 = 14
for n = 3
f(4) = f(3) - 2 = 14- 2 = 12
for n = 4
f(5) = f(4) - 2 = 12-2 = 10
Therefore, For the above sequence, f(5) will have the value of 10.
Learn more about sequence here:
https://brainly.com/question/28615767
#SPJ2
please help 80 points for 2 questions please answer all parts and show your work! due today!!!!
Part A
The scatterplot is shown the attachment.
Part B
Using a linear regression equation that models Patrick's referrals has a positive slope.
This means that, there is a positive relation between time(number of days),x and the number of personal recommendations, y.
In other words, as the number of days increases, the number of personal recommendations also increases.
Question 2.
The given functions are:
[tex]y=x^2+3x-5[/tex]
[tex]y=4x+1[/tex]
To find the point where the graphs of these functions intersect,we solve the two equations simultaneously.
We equate the two equations to get:
[tex]x^2+3x-5=4x+1[/tex]
[tex]x^2+3x-4x-5-1=0[/tex]
[tex]x^2-x-6=0[/tex]
Factor to obtain:
[tex](x-3)(x+2)=0[/tex]
x=3 and x=-2
We put x=-2, into [tex]y=4x+1[/tex] to get;
[tex]y=4(-2)+1=-7[/tex]
when x=3 [tex]y=4(3)+1=13[/tex]
Therefore the graphs intersect at (-2,-7) and(3,13).
Yes, solution is correct.
what times what gives me -48 but adds to be -32?
Answer:
a couple of irrational numbers: -16±4√19, approximately {1.436, -33.436}
Step-by-step explanation:
Your question can be cast as the quadratic equation
x² +32x -48 = 0
The solutions can be found using the quadratic formula:
x = (-32 ±√(32² -4(1)(-48)))/(2(1)) = -16±√304 = -16±4√19
_____
Comment on the equation we used
We notice that when p and q are roots, the equation can be written ...
(x -p)(x -q) = 0 = x² -(p+q)x +pq
You want p+q = -32, pq = -48, so the equation is ...
x² -(-32)x +(-48) = 0
x² +32x -48 = 0 . . . . . . with parentheses eliminated
Which system of linear inequalities has the point (3,-2) in its solution set?
A.y < -3
y ≤ 2/3x - 4
B.y > -3
y ≥ 2/3x - 4
C.y < -3
y ≥ 2/3x - 4
D.y > -2
y ≤ 2/3x - 4
(the answers come with graphs but sorry I couldn't find a way to put them all in)
Answer:
Option B.
Step-by-step explanation:
we know that
If a ordered pair is a solution of the system of inequalities
then
the ordered pair must satisfy both inequalities of the system
Verify each case
Case A) we have
The point (3,-2)
Substitute the value of x and the value of y in both inequalities and then compare the results
Inequality 1
[tex]-2< -3[/tex] ----> is not true
therefore
The ordered pair is not a solution of the system A
Case B) we have
The point (3,-2)
Substitute the value of x and the value of y in both inequalities and then compare the results
Inequality 1
[tex]-2> -3[/tex] ----> is true
Inequality 2
[tex]-2 \geq \frac{2}{3} (3)-4[/tex]
[tex]-2\geq -2[/tex] ----> is true
therefore
The ordered pair is a solution of the system B
Case C) we have
The point (3,-2)
Substitute the value of x and the value of y in both inequalities and then compare the results
Inequality 1
[tex]-2<-3[/tex] ----> is not true
therefore
The ordered pair is not a solution of the system C
Case D) we have
The point (3,-2)
Substitute the value of x and the value of y in both inequalities and then compare the results
Inequality 1
[tex]-2>-2[/tex] ----> is not true
therefore
The ordered pair is not a solution of the system D
Answer:
i think it is b as well! on edg
Step-by-step explanation:
Point O is the center of the circle in the diagram. What is m/_BCA
Answer:
< BCA = 70
Step-by-step explanation:
The complete central angle of a circle is 360 degrees. The given portion is 250 degrees.
What is left over? BOA = 360 - 250 = 110
Tangents always meet the radius at 90 degrees. Since there are two tangents <CAO = <BAO = 90 degrees.
So piecing it all together, the equation becomes
<BAO + CAO + BAO + ACB = 360
110 + 90 + 90 + <ACB = 360
290 + <ACB = 360
<ACB + 290 - 290 = 360 - 290
ACB = 70 degrees
The lengths of trout in a lake are normally distributed with a mean of 30 inches and a standard deviation of 4.5 inches.
Enter the z-score of a trout with a length of 28.2 inches.
Answer:
-0.4
Step-by-step explanation:
z score is:
z = (x - μ) / σ
For x = 28.2, μ = 30, and σ = 4.5:
z = (28.2 - 30) / 4.5
z = -0.4
Answer: -0.4
Step-by-step explanation:
Given: Mean : [tex]\mu=30\text{ inches}[/tex]
Standard deviation : [tex]\sigma=4.5\text{ inches}[/tex]
The formula to calculate z-score is given by :-
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
For X = 28.2 inches, we have
[tex]z=\dfrac{28.2-30}{4.5}\\\\\Rigahtarrow\ z=-0.4[/tex]
Hence, the z-score of a trout with a length of 28.2 inches.= -0.4
The volume of a sphere is 2 comma 143.57 m cubed. To the nearest meter?, what is the radius of the? sphere? Use 3.14 for pi.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \stackrel{\pi =3.14}{\cfrac{6430.71}{4(3.14) }}=r^3\implies 511.9992\approx r^3 \\\\\\ \sqrt[3]{511.9992}\approx r\implies 7.999996\approx r\implies \stackrel{\textit{rounded up}}{8=r}[/tex]
According to Boyle’s law, PV= K, what was the volume at the time of the first measurement given the following information? Round to the nearest mL.
P1=5.42 atm
P2=8.59 atm
V2=527 mL
The answer is:
The first measurement of volume is equal to 835.23 mL.
Why?Boyle's Law equation can be used when the temperature is kept constant, and it establishes a relation between the pressure and volume, showing that when an ideal gas is kept constant, the pressure and volume are inversely proportional.
So, we Boyle's Law equation states that:
[tex]P_{1}V_{1}=P_{2}V_{2}[/tex]
Where,
[tex]P_1=FirstPressure\\V_1=FirstVolume\\P_2=NewPressure\\V_2=NewVolume[/tex]
Now, if we are looking for the first volume measurement, we need to rewrite the equation as follow:
[tex]P_{1}V_{1}=P_{2}V_{2}\\\\V_{1}=\frac{P_{2}V_{2}}{P_{1}}[/tex]
So, substituting the given information and calculating, we have:
[tex]V_{1}=\frac{8.59atm*527mL}{5.42atm}[/tex]
[tex]V_{1}=\frac{4526.93atm.mL}{5.42atm}=835.23mL[/tex]
Hence, the first measurement of volume is equal 835.23 mL.
Have a nice day!
The Earth completely rotates on its axis once every 24 hours.
A) How long does it take for it to rotate 310 degrees?
B) How long does it take to rotate 5 radians?
C) The diameter of the Earth is approximately 7920 miles. How far will a point on the equator rotate in 2 hours?
Show all work. Give answers to the nearest hundredth. Include the units in your response.
Answer:
Part A). 20 hours 42 minutes taken by earth to rotate 310°.
Part B). 19 hours 6 minutes taken by earth to rotate 5 radians.
Part C). 2072.4 miles a point on the equator rotate in 2 hours.
Step-by-step explanation:
Given : Earth rotate 360° in 24 hours.
Part A).
Time taken by earth to rotate 360° = 24 hours.
Time taken by earth to rotate 1° = [tex]\frac{24}{360}[/tex] hours.
Time taken by earth to rotate 310° = [tex]\frac{24}{360}\times310[/tex] hours.
= 20.7 hours = 20 hours 42 minutes (approx.)
Part B).
Time taken by earth to rotate 360° = 24 hours.
We know that 360° = 2π radian
Time taken by earth to rotate 2π radian = 24 hours.
Time taken by earth to rotate 1 radian = [tex]\frac{24}{2\pi}[/tex] hours.
Time taken by earth to rotate 5 = [tex]\frac{24}{2\pi}\times5[/tex] hours.
= 19.098 hours = 19 hours 6 minutes (approx.)
Part C).
Diameter of Earth = 7920 miles
Radius of Earth, r = 7920/2 = 3960 miles.
Degree of rotation in 24 hour = 360°
Degree of rotation in 2 hour, [tex]\theta\:=\frac{360}{24}\times2=30^{\circ}[/tex]
Now use Formula used to calculate Length of the arc of the circle.
Length of the Arc = [tex]\frac{\theta}{360}\times2\pi r[/tex]
Length a point on equator moves in 2 hour = [tex]\frac{\theta}{360}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]
Dewight is proving the sum formula for the sine function. He has started his proof, what property should he use to complete the next line?
Answer:
C) the difference identity for the cosine function
Step-by-step explanation:
The last line showing shows the cosine of the difference of two angles. The difference identity for the cosine function would seem to be indicated.
Which is a reason to save money regularly?
A. You will always have a steady income source
B. You need access to funds for frivolous spending
C. You can qualify for opportunities that might otherwise be impossible
D. You can pay less with credit purchases
(my answer is D)
Answer:
The answer is C I believe
Answer:
C. You can qualify for opportunities that might otherwise be impossible
What is an equation for a sine curve with amplitude 2
ANSWER
[tex]y = 2 \: \sin(x) [/tex]
EXPLANATION
A basic sine curve has equation in the form:
[tex]y = a \: \sin(x) [/tex]
Where 'a' is the amplitude.
In this case a=2 because the amplitude is 2.
[tex]y = 2 \: \sin(x) [/tex]
For a transformed sine function, the general equation is:
[tex]y = a \: \sin(bx + c) + d[/tex]
where a=2 is still the amplitude
[tex]y = 2 \: \sin(3x + \pi) [/tex]
This is also a sine function with an amplitude of 2.
Others include:
[tex]y = 2 \: \sin(x + 1) [/tex]
[tex]y = 2 \: \sin(4x - \pi) [/tex]
e.t.c
A square has side length of 16.5 in. If the area is multiplied by 9, what happens to the side length?
Answer:
The side length is multiplied by the scale factor of 3, which makes it 49.5
Step-by-step explanation:
The scale factor goes as follows
length : scale factor
area: scale factor squared
Volume : scale factor cubed
Since we increased the area by 9, that would be the scale factor squared
Take the square root of 9, which is 3, and that is the scale factor
We want to know what happens to the length
It is multiplied by the scale factor
16.5*3 = 49.5
The wheels on Kiran's bike are 64 inches in circumference. How many times do the wheels rotate if Kiran rides 300 yards?
Answer:
168.75, about 169 times
Step-by-step explanation:
1 yd= 36 in
300 yd= 10800 in
10800 in/ 64 in=168.75
Answer:
169
Step-by-step explanation:
We are given that
Circumference of Kiran's bike wheel=64 in
Kiran rides total distance=300 yards
We have to find number of rotations made by wheel.
We know that
1 yard=36 in
300 yards=[tex]36\times 300=10800 in[/tex]
Number of rotation=[tex]\frac{Total\;distance\;covered\;by\; wheel}{Circumference\;of\;wheel}[/tex]
Number of rotations=[tex]\frac{10800}{64}=168.75\approx 169[/tex]
Hence, the wheel rotate=169 times