Put the numbers in order from least to greatest. 1.5 × 104, 2.6 × 10-2, 3.5 × 102, 6.2 × 10-1

Answers and Step-by-step explanations:

(a) We want to find the slope-intercept equation (y = mx + b), where m is the slope and b is the y-intercept. We already have two points: (2, 6200) and (7, 21200). The slope is change in y over change in x so:

m = (21200 - 6200) / (7 - 2) = 3000

Now, we have y = 3000x + b. Plug in 6200 for y and 2 for x to solve for b:

y = 3000x + b

6200 = 3000 * 2 + b

b = 200

Nat's equation is y = 3000t + 200.

(b) We want a quadratic formula in vertex form because the problem says that Kat's account maxes out at 44100 on her 25th birthday, indicating that's the vertex. Our vertex point is (20, 44100); note that it's 20 and not 25 because she starts the account at age 5, not age 0. The generic vertex form of a quadratic is:

y = a(x - h)² + k, where (h, k) is the vertex

Plug in our vertex:

y = a(x - 20)² + 44100

We also have the point (9, 32000), so put that in to find a:

32000 = a(9 - 20)² + 44100

-12100 = a * 121

a = -100

So Kat's equation is y = -100(t - 20)² + 44100.

(c) In order to find the age when they have the same amount, we set the two equations equal:

3000t + 200 = -100(t - 20)² + 44100

-100(t² - 40t + 400) + 44100 = 3000t + 200

-100t² + 4000t - 40000 + 44100 - 3000t - 200 = 0

-100t² + 1000t + 3900 = 0

t² - 10t - 39 = 0

(t - 13)(t + 3) = 0

t = 13 or t = -3   --   obviously, years can't be negative, so t = 13.

Note, however, that t is the number of years after Kat and Nat are 5, so we need to add 13 to 5:

13 + 5 = 18

The age is 18.

A: [tex]N(t) = 3000t +200[/tex]

B: [tex]y = -100(x-20)^2+44100[/tex]

C: When they turn 18.

A. Write a linear function N(t) for the amount of money, N, that Nat has in her account ‘t’ years after her 5th birthday:

You can determine a linear equation using the two coordinates provided:

(2, 6200) and (5, 21200).

To do this, first find the slope of the graph. You can do this by using the expression

[tex]\frac{y2-y1}{x2-x1}[/tex], where the coordinate (2, 6200) is 1 and (7, 21200) is 2:

[tex]\frac{21200-6200}{12-7}\\\\\frac{15000}{5}[/tex]

The slope is equal to 3000. Now, you need to find the y-intercept. Plug in 2 for x and see what the y intercept would need to be to equal 6200:

6200 = 3000 * 2 + b

6200 = 6000 + b

b = 200

Thus, your equation for Nat's bank account is [tex]N(t) = 3000t + 200[/tex]

B: Kat’s account doesn’t follow a linear model, but rather a quadratic model. On her 5th birthday, her parents open the account and then add money annually just like with Nat. Kat’s parents plan is to add money so that her account maxes out at $44100 on her 25th birthday. At the age of 14, she has $32000. Write a quadratic function K(t) for the amount of money, K, in Kat’s account ‘t’ years after her 5th birthday:

The question supplies you with the vertex to the parabola, (20, 44100). This is the point at which the maximum value of the function is reached.

It also supplies you with a point on the parabola, (9, 32000).

You can use the vertex form of the quadratic equation to find the formula for Kat's bank account:

[tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.

Substituting the vertex in for that equation, we get:

[tex]y=a(x-20)^2+44100[/tex]

Now, you can substitute the point (14, 32000) in for x and y to solve for a:

[tex]32000=a(9-20)^2+44100\\\\-12100 = 121a\\a = -100[/tex]

Thus, the equation is [tex]y = -100(x-20)^2+44100[/tex].

C. What age will both Nat and Kat have the same amount in their account? 18 years old.

To find what age each account will be equal, set the equations equal to each other:

[tex]-100(x-20)^2+44100 = 3000x +200[/tex]

Then, you can solve for x:

[tex]-100(x-13)(x+3)=0[/tex]

Solving for x, we notice that the accounts equal each other when Nat and Kat are -3 or 13. However, Nat's function is only specified to begin after she turns 5, so add 5 to 13 to get 18.

They will both have the same money in their accounts when they turn 18.

Answer:

C

Step-by-step explanation:

Answer:

B on edge

Step-by-step explanation:

Answer:

Volume of the pipe = 423.9cm³

Step-by-step explanation:

Width = 6cm = diameter

Radius (r) = d / 2 = 6 / 2 = 3cm

Height = 15cm

Volume = ?

π = 3.14

Assuming the shape of the pipe is that of a cylinder, then we can easily find its volume just by calculating the volume of the cylinder.

Volume of a cylinder = πr²h

π = 3.14

r = radius of the cylinder

h = height of the cylinder

Volume = 3.14 × 3² × 15

Volume = 3.14 × 9 × 15

Volume = 423.9cm³

The volume of the pipe is 423.9cm³

The volume of the given pipe is [tex]424.12\ cm^3[/tex].

To calculate the volume of the pipe, assume the pipe is cylindrical and use the formula for the volume of a cylinder. The formula is given by:

[tex]V = Area\ of\ cross\ section \times height[/tex]

Since the pipe is cylindrical, the cross section is a circle. Therefore:

[tex]Area\ of\ cross\ section = \pi r^2[/tex]

where r = radius of cross section

Given width = 6 cm = diameter of the cross section = 2r

[tex]2r = 6\ cm \implies r = \frac{6}{2}\ cm = 3\ cm[/tex]

Therefore:

[tex]Area\ of\ cross\ section=A = \pi r^2 = \pi (3)^2 = 9\pi\ cm^2[/tex]

Assuming the 'height' mentioned is the length through which fluid is flowing, and given the cross-sectional area, the volume formula simplifies to:

[tex]V = A\times h[/tex]

Given height (length of cylinder) = 15 cm:

[tex]V = 9\pi \times 15\ cm^3 = 135\pi \ cm^3 \approx 424.12\ cm^3[/tex]

So, the volume of the pipe, assuming it as cylindrical, is [tex]424.12\ cm^3[/tex].

Answer:

make it polynomial eqution and than solve it for x

Step-by-step explanation:

hope this will help you

Answer:

10x² - 11x - 6

Step-by-step explanation:

(5x+2)(2x-3)

10x² + 4x - 15x - 6

10x² - 11x - 6

Initial ratio W/Y=1

new ratio (w+30)/y=6/5, or substituting w for y you get 6w=5w+150 or w=150.

then y=150, so the shop ordered 300 balls initially, 150 each

Hope this helped

:)

Answer:

169

Step-by-step explanation:

13^2 is really just 13 times 13 which equals 169

Answer:

35%

Step-by-step explanation:

8+12+14+6=40

8+6=14

p( pizza or steak)=14/40=0.35

0.35*100=35%

The experimental probability is the occurrence probability of an event concerning all events. The experimental probability of pizza or steak is P(P or B) = 35%

The experimental probability is a probability assigned to an event. It is the number of times an event occurs concerning the number of times all events occur or the experiment is repeated.

It can be calculated by taking the relative frequency of the event when the experiment is repeated several times.

To calculate it, we can use the following formula,

P(E) = Number of trials performed in which a certain event occurred / Total number of trials in which all events occurred

In the exposed example,

steaks.

P(E) = Number of trials performed in which a certain event occurred / Total number of trials in which all events occurred

P(P or B) = (8 + 6) / (8 + 12 + 14 + 6) = 14 / 40 = 0.35 = 35%

The experimental probability of pizza or steak is P(P or B) = 35%

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The surface area of the composite figure shown is 356 square feet. So, option b) is correct.

Surface area is the total area covered by the surface of the figure.

Given, the composite figure can be converted into two figures as shown in the image attached below:

Total Surface area of the composite figure= Area of figure 1 +  Area of figure 2.

Area of figure 1= Area of I+ Area of G+ Area of H+ Area of F

Area of I= Area of G

= Area of triangle

[tex]=\dfrac{1}{2}b\times h[/tex]

=7 x 4/2

=14

Area of I= Area of G

=8 x 4/2

=16

Area of figure 1= 14+14+16+16

Area of figure 1=60 sq feet

Area of figure 2 = Area of A+Area of B+Area of C+Area of D+Area of E

Area of rectangle=l x b

Area of A=Area of B=Area of D

=7 X 8

=56

Area of C=Area of E

=8 X 8

=64

Area of figure 2 = 56+56+64+56+64

Area of figure 2 = 296 sq feet

Surface area of the composite figure=296+60

=356 square feet

Thus, surface area of the composite figure is 356 square feet. So, option b) is correct.

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Answer: D arccsc(x) = arcsin(1/x)

Step-by-step explanation:

The correct equation is arccsc(x) = arcsin(1/x), as it represents the inverse relationship between the cosecant and sine functions, indicating that arccsc(x) finds the angle whose sine is the reciprocal of x.

The correct equation related to arcsecant is arccsc(x) = arcsin(1/x). The arcsecant function, arccsc(x), is the inverse of the cosecant function, csc(x), which is the reciprocal of the sine function, sin(x). Therefore, arccsc(x) is used to find the angle whose cosecant is x. Since csc(x) = 1/sin(x), taking the inverse of both sides, we get arccsc(1/sin(x)) = x. By further manipulation, we can say that arccsc(x) = arcsin(1/x) because we are essentially finding the angle whose sine is the reciprocal of x.

The equation arccsc(x) = 1/sin(x) suggests a relationship between arccsc and the sine function directly, but this would imply that arccsc(x) gives us the value of 1/sin(x), which is not the case. The correct interpretation is that arccsc finds the angle whose cosecant (which is 1/sin(x)) is x, hence the equation arccsc(x) = arcsin(1/x).

Answer:

mean = 6.4

median = 6.5

range = 9

Step-by-step explanation:

hope this helps!!

Answer:

Step-by-step explanation:

Mean = Sum of scores/number of games

[tex]=\frac{4+10+7+9+2+11+4+9+2+6}{10}\\\\=\frac{64}{10}\\\\[/tex]

Mean = 6.4

4,10,7,9,2,11,4,9,2,6

Ascending order: 2,2,4,4,6,7,9,9,10,11

Median is the middle term. As number of terms is even number (10),

We have to find the mean of middle terms. ie median of 5th and 6th term

[tex]Median=\frac{6+7}{2}\\\\=\frac{13}{2}[/tex]

Median = 6.5

Range = Maximum score - minimum score

  = 11 - 2

Range = 9

Answer:

2b -a

a-2c

Step-by-step explanation:

a = b+c

We want to find b-c

Solve the first equation for b

b = a-c

and for c

c = a-b

b-c in terms of b and a  

using c = a-b

b - (a-b)

Distribute the minus sign

b - a +b

Combine like terms

2b -a

b-c in terms of c and a  

using b = a-c

(a-c) -c

a-c -c

Combine like terms

a-2c

Answer:

about $215

Step-by-step explanation:

Answer:102

Step-by-step explanation:

180-36=144

x+42=144

x=102

The measure of x from the circle is x = 102

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

r is the radius of the circle

Central Angle = 2 x Angle in other segment

Given data ,

Let the measure of the external angle ∠GDF = 36°

Now , Central Angle = 2 x Angle in other segment

And , the measure of ∠GAF = ( x + 42 )°

On simplifying , we get

( x + 42 )° = 180° - 36°

x + 42 = 144

Subtracting 42 on both sides , we get

x = 102

Hence , the measure of x of circle is 102

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Answer:

C

Step-by-step explanation:

its a wild guess because you didn't add a picture or anything to show the  pyramid

Answer:

i think it's b

Step-by-step explanation:

Answer: I think it is High overlapped

Step-by-step explanation: because when comparing it look like a small difference between them.

Answer:

f(x) = sin(x)+4

Answer:

-5 < - 4 is correct

Step-by-step explanation:

I5I > 7 is wrong because I5I < 7

7 < I7I is wrong .  7 = I7I

I-3I > I-4I  is wrong because absolute value is always positive.

So I-3I < I-4I

Answer:

5<-4

Step-by-step explanation:

Answer:

6 weeks

Step-by-step explanation:

You can use linear equations to find this out.

y is the total amount saves, x is the number of weeks.

Jade's equation: y = 5x + 0 (the 5 is how much she will save each week, the 0 is how much she has now, or the initial value.)

Enrique's equation: y = 3x + 12 (the 3 is how much he will save each week, the 12 is how much he has now, or the initial value.)

You can set up a table, or you could enter it in your calculator.

After entering the equations in my calculator, I found that the x value of 6 was when both equations had the same y value. So after 6 weeks, both of them had saved 30 dollars.

Answer:

Step-by-step explanation:

3(y + z)

2y + 2z + y + z

Answer:

37.7cm

Step-by-step explanation:

Answer:[tex]12\pi[/tex]

[tex]12\pi[/tex]

Step-by-step explanation:

The formula is: [tex]C= 2\pi r[/tex]

Diameter is the same has 2r, r being the radius.

To help remember: Cherry Pies ([tex]\pi[/tex]) Are (r) Too.

Answer:

Base x height = area

3.7 x 5 = 18.5

18.5 is the area

Step-by-step explanation:

Answer:

It's geometric

Step-by-step explanation:

You multiply each term by "-3," so the common ratio is -3, making the sequence geometric.

Answer:

m = 40.5

Step-by-step explanation:

21/8.1 = 105/m

Croos multiplying the fractions, we get

21m = 850.5

m = 850.5/21

m = 40.5

hope it helps!

To solve the proportion 21/8.1 = 105/m, cross-multiply to get 21m = 850.5. Then, divide both sides by 21 to find m = 40.5.

To solve the equation 21/8.1 = 105/m, you can use cross-multiplication. By setting up the proportions correctly, you ensure that meters, being the only unit involved, is properly handled in the calculations.

First, cross-multiply to get 21 * m = 105 * 8.1. This simplifies to 21m = 850.5. Next, divide both sides of the equation by 21 to isolate m on one side, leaving you with m = 850.5 / 21. Upon dividing, you get m = 40.5.

It's important to remember that when dealing with ratios or proportions, canceling equivalent terms in the numerator and denominator simplifies the problem, making it easier to solve. Moreover, understanding how to deal with powers of 10 is essential, such as knowing that for 105/103 = 105-3 = 102 is helpful in many mathematical problems.

Answer:

perfect negative correlation

Step-by-step explanation:

correlation coefficient is the term used in statistic which provides the information of strength of relation between two variables. This value suggests if there is change in value of one variable, what will be the change in the variable and how much will value of that change.

What will be the change : it suggest whether change in value of one variable other will be increase or decrease .

If there is increase in one variable and other also increases it suggest there is positive correlation .

If there is decrease in one variable and other also decrease it suggest there is positive correlation .

how much will value of that change: It means to say if there is change in one variable by how much amount other variable will change.

If the value of correlation coefficient is high it means that  change in value   for one variable is high in to  response change in other variable .

It values ranges from -1 to +1 high

while sign depicts type of relation that is positive or negative .

value from - 1 to + 1 depicts strength of the relation .

with - 1 depicting  perfect negative correlation

+1   depicting perfect positive correlation.

In the problem it is given correlation coefficient is 1 which means it is positive and value of one means that if there x percentage increase in one variable then other variable will also increase by x percentage and vice versa.

Answer:

I think Answer is  B

Step-by-step explanation:

Answer:

[tex]n=\frac{0.93(1-0.93)}{(\frac{0.09}{1.96})^2}=30.875[/tex]  

And rounded up we have that n=31

Step-by-step explanation:

First we need to find the critical value for the margin of error desired. The confidence level is 0.95 so then the significance is [tex]\alpha=1-0.95=0.05[/tex] and the critical value for this case would be:

[tex] z_{\alpha/2} =\pm 1.96[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.09[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

The estimated proportion for this case is [tex]\hat p =0.93[/tex]. And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.93(1-0.93)}{(\frac{0.09}{1.96})^2}=30.875[/tex]  

And rounded up we have that n=31

Answer:

A.6.96 B. .3629 C.8.7

Step-by-step explanation:

i used calculator plz brainliest

Answer:

A. 125.28

B. 1 apple = $3.26

C. 156.48

Step-by-step explanation:

A. $2.61 * 48 [(12 apples = 1 dozen) times 4 equals 4]= 125.68

B. 2.61/1 * 25/100= 65.25/100      (25% = 25/100)

65.25/100= 0.6525

0.6525= 0.65

$2.61 + $0.65 = $3.26/ apple

C. $3.26 * 48( see above on problem A)= $156.48

[tex] {8}^{ - 1} = \frac{1}{8} [/tex]

8-¹ ❌

[tex] {9}^{ - 2} = \frac{1}{ {9}^{2} } = \frac{1}{81} [/tex]

9-² ✔️

[tex] \frac{ {9}^{8} }{ {9}^{4} } = {9}^{8 - 4} = {9}^{8} [/tex]

9^8/9^4 ❌

[tex] \frac{9 {}^{8} }{ {9}^{10} } = {9}^{8 - 10} = {9}^{ - 2} = \frac{1}{9 {}^{2} } = \frac{1}{81} [/tex]

9^8/9^10 ✔️

[tex] {9}^{ - 6} \times {9}^{3} = {9}^{ - 6 + 3} = {9}^{ - 3} = \frac{1}{9 {}^{3} } = \frac{1}{729} [/tex]

9^-6 . 9³ ❌

[tex] {9}^{5} . \: { 9}^{ - 7} = {9}^{5 - 7} = 9 {}^{ - 2} = \frac{1}{ {9}^{2} } = \frac{1}{81} [/tex]

9^5 . 9^-7 ✔️