Write a linear function with the values f(0) = - 5 and f(3) = 4

Answer:

1. 3 1/5

2. 1/4 1/5 1/6 1/7 1/8

3. (a) 32/49 (b) 7/16

4. 11/16

5.(i) 20/35 (ii) 16/28

6. 3/4 is bigger than 2/5 because if you convert then 3/4=15/20 and 2/5=8/20

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

The statements that can be made about the parabola are;

The parabola opens towards the right

The equation of the parabola is (y - 1)² = 16 × (x + 1)

The parabola has a vertex at (-1, 1)

Step-by-step explanation:

The given focus of the parabola is (3, 1)

The directrix of the parabola, x = -5

Therefore, from the location of the directrix (on the x-axis) and the location of the focus relative to the directrix towards the positive direction of the x-axis relative to the directrix, the parabola opens towards the left of the coordinate chart

The general equation of the focus = (h + p, k)

The general equation of the directrix, x = h - p

Comparing with the values of the focus and the directrix of the given parabola, we have;

(3, 1) = (h + p, k)

-5 = h - p

Therefore, we get;

k = 1

h + p = 3...(1)

h - p = -5...(2)

Adding equation (1) to equation (2) gives;

h + h + p - p = 3 + (-5)

2·h = -2

h = -2/2 = -1

h = -1

From equation (1), we get;

h + p = -1 + p = 3

∴ p = 3 + 1 = 4

p = 4

The vertex of the parabola, (h, k) = (-1, 1)

The equation of the parabola in the form (y - k)² = 4·p·(x - h) is therefore, presented as follows;

The equation of the parabola = (y - 1)² = 4 × 4 × (x - (-1))

(y - 1)² = 16 × (x - (-1))

The equation of the parabola is (y - 1)² = 16 × (x + 1).

Answer:

Theoretically, since it has two sides, it's a 50 50, chance. 50%

Answer:

32.56

Step-by-step explanation:

I think that's the area.

Answer:

last option:  y = -2/7x + 4

Step-by-step explanation:

original equation, in slope-intercept form, is:  y = -2/7x -8

Parallel lines have equal slopes

Answer:

A= -17

Step-by-step explanation:

A +-21 = -38

    +21     +21

-38+21= -17

A= -17

Answer:

a = -17

Step-by-step explanation:

To solve this, we need to get A alone:

A + -21 = -38

—- +21- +21

Remember, when you do something to one side, you need to do the same thing to the other side.

Now:

A = -17!

To check:

-17 + -21 = -38

Therefore, A = -17

Answer: I think the answer is b but I'm not sure

Step-by-step explanation:

Answer: 37.5%

Step-by-step explanation:

Percentage = Given Quantity/Total Quantity*100

So here, it will be like: 45/120*100

                                    =0.375*100

                                    =37.5%

Using t-test, there isn't an enough evidence to support our claim that investment average is $135,000 at α = 0.05.

The one sample t test compares the mean of your sample data to a known value (population mean in our question, i.e. , we wish to compare the sample mean with the population mean). One sample t test should be used when you the population standard deviation is not known or the sample size is very small.

Assumptions of the t-test for the test to be valid:-

Null hypothesis:  μ = $143,260

Alternative hypothesis: μ < $143,260

Calculating test statistic.

n = 30

sample mean = $135,000

sample standard deviation = $30,000

[tex]t_{0} = \frac{sample\ mean - population\ mean}{\frac{standard\ deviation}{\sqrt{sample\ size} } }[/tex]

[tex]t_{0} = \frac{135000 - 143260}{\frac{30000}{\sqrt{30} } }[/tex]

|to| = 1.508

Test criteria:

level of significance = 0.05

t(0.05, 29) = 1.6991

Since, |to| = 1.508 < t(0.05, 29) = 1.6991, null hypothesis cannot be rejected.

Learn more about t-test here

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Answer:

C

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

We can expect that 4 of the next 20 pies sold will be blackberry pies, based on the proportion of blackberry pies in the recent sample of 15 pies.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

If Tracy's Pie Shop recently sold 15 pies and 3 of them were blackberry pies.

Proportion of blackberry pies = 3/15

Proportion of blackberry pies = 0.2

So, in the recent sample of 15 pies, 20% were blackberry pies.

To estimate how many of the next 20 pies sold should be blackberry pies

Let us assume that the proportion of blackberry pies in the next sample of 20 pies will be similar to the proportion in the recent sample of 15 pies.

Therefore, we can use this proportion to estimate the number of blackberry pies in the next sample of 20 pies:

Number of blackberry pies = 0.2 x 20

Number of blackberry pies = 4

Therefore, we can expect that 4 of the next 20 pies sold will be blackberry pies, based on the proportion of blackberry pies in the recent sample of 15 pies.

To learn more on Ratios click:

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Answer:

Step-by-step explanation:

As two sides are equal so angles opposite to these are also equal, hence

5x-4=x+52

4x=56

X=14

Now,

R=5x-4

R=66

And,Q=x+52

Q=66(we already knew both angles are equal)

Now as sum of all angles of triangle equal 180 so,

66+66+P=180

P=48

Answer:

Step-by-step explanation:

y=2x because

3x2 =6

10x2=20

12x2=24

17x2=34

I hope it's the right answer .

Answer:

h = 38

Step-by-step explanation:

[tex] \frac{h + 52}{70} = \frac{9}{7} [/tex]

[tex]h + 52 = \frac{9}{7} \times 70[/tex]

[tex]h + 52 = \frac{9 \times 70}{7} [/tex]

[tex]h + 52 = \frac{630}{7} [/tex]

[tex]h + 52 = 90[/tex]

[tex]h = 90 - 52[/tex]

[tex]h = 38[/tex]

the answer is 38.

Answer:

16.49 feets

Step-by-step explanation:

Using Pythagoras rule, we could find, h the height of the wall ;

Using the relation :

a² = b² + c²

36² = h² + 32²

1296 = h² + 1024

h² = 1296 - 1024

h² = 272

h = √272

h = 16.49 feets

Step-by-step explanation:

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Answer:

8.73 units

Step-by-step explanation:

Use the area formula, A = lw

Plug in the are and given side length, and solve for w

A = lw

24 = 2.75w

Divide each side by 2.75

8.73 = w

The other side length of the rectangle is approximately 8.73 units

Answer:

x=23/3 and y=-7/3

Step-by-step explanation:

So it would be (23/3,-7/3)

Answer:

3.25

Step-by-step explanation:

Divide 104 by 32

Answer:

3.25 or 3 1/4

Step-by-step explanation:

"By what number must I multiply 32 to get 104?"

Divide 104 by 32:  3.25 or 3 1/4

Answer: 5

Step-by-step explanation:

Answer:

6.3 yards

Step-by-step explanation:

mathematically, to get the circumference of the circle, we will have to use the formula for the circumference of a circle

we have this as;

C = 2 * pi * r

r is 1 yard

c = 2 * pi * 1 = 2pi yards = 6.3 yards

Answer:

y=kx

Step-by-step explanation:

For this example it would be [tex]y=\frac{72}{2} x\\[/tex] or y=36x

Answer:

90 kittens

Step-by-step explanation:

Find the percent of cats that are kittens using the 12 out of 20.

12/20 = 0.6 = 60%

Now, find 60% of 150 cats.

150 • 0.6 = 90 kittens

Answer:

First you should divide 20-12=8 Then *18.75*

That would be the answer

Step-by-step explanation:

Hope This Helps!!! :)

Hello there!

I used a calculator for this problem, but it shows you the steps involved. The picture is included. I hope this helps!

Answer:

Step-by-step explanation:

1 and 2/3 rotations. The little gear full rotation is equal to 1/6 of the big gears rotation. So if the big gear rotates once then its equal to 6 of the small rotations the extra 4 of the 10 rotations then becomes 4/6 of the big gears rotation or if simplified further, 2/3. This is my way of solving these questions

Answer:

A=30cm^2

Step-by-step explanation:

Area of a parallelogram is base X height

in this diagram base = 10 cm

height = 3 cm

3 X 10 = 30

Answer:

30 cm^2

Step-by-step explanation:

Formula of parallelogram = base * height

height = 3

base = 10

10(3) = 30

Answer:

5 miles

Step-by-step explanation:

2.3 miles south

then 4.5 miles east

a^2 + b^2 = c^2

a = 2.3 miles

b = 4.5 miles

(2.3)^2 + (4.5)^2 = c^2

c^2 = 25.54

[tex]\sqrt{c^2}[/tex] = [tex]\sqrt{25.54}[/tex]

c = 5.0