Use the 200 Meter Dash
graph to answer the
following questions about
Runner A
Runner B
1. Which runner won the race?
Distance (m)
250
200
150
100
50
0
200 Meter Dash
05
C
10 15 20 25
Time (sec)
2. Which runner had a bad start to his race?
3. Which runner was the fastest at the start of the race?
a runner C
b. runner A
C. runner B

The requirements for a hypothesis test are satisfied.

To test the claim that the rate of polio is less for children given the Salk vaccine, we need to check if the requirements for a hypothesis test about two population proportions are met. The requirements are:

1. The samples are simple random samples and independent.
2. For each of the two groups, the sample size is at least 1000.

In this case, the study involved 401,974 children who were randomly assigned to two groups: the treatment group with 201,229 children and the placebo group with 200,745 children. This satisfies the first requirement, as the samples are simple random samples and independent. The sample size for both groups is also larger than 1000, meeting the second requirement.

Therefore, the requirements for a hypothesis test are satisfied, and we can proceed with testing the claim that the rate of polio is less for children given the Salk vaccine.

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The total surface area of the pyramid is  1,296 unit².

The lateral surface area (L.A) of the pyramid is 19.21 unit².

The volume of pyramid is 120 unit³.

The surface area of the pyramid is calculated as follows;

T.S.A = 2bh + b²

where;

In then diagram, we where given, base, b = 24 units, height = 15 units, then the surface area of the pyramid is calculated as follows;

T.S.A = 2 x 24 x 15  +  24²

T.S.A = 1,296 unit²

The lateral surface area is calculated as

L.A = √(b²/4 + h²)

L.A = √(24²/4 + 15²)

L.A = 19.21 unit²

The volume of pyramid is calculated as;

V = ¹/₃BH

V = ¹/₃ x 24 x 15

V = 120 unit³

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Answer:

[tex](x - 9)(x - 1)[/tex]

Step-by-step explanation:

We can factor the trinomial using the rule:

IF [tex]x^2 + cx + d = (x + a)(x + b)[/tex],

THEN [tex]a + b = c[/tex] and [tex]a \cdot b = d[/tex].

We know that -9 and -1 add to -10. They also multiply to 9.

Therefore, we can factor [tex]x^2 - 10x + 9[/tex] as:

[tex]\boxed{(x - 9)(x - 1)}[/tex]

The factors of the given trinomial are (x-9)(x-1).

Trinomial is a polynomial having 3 terms. At least one variable and one operation (addition, subtraction, multiplication, division) must be present in an algebraic expression.

Given that, a trinomial x² - 10x + 9, we need to find the factors,

So,

x² - 10x + 9

= x² - 9x - x + 9

= x(x-9) -1(x-9)

= (x-9)(x-1)

Hence, the factors of the given trinomial are (x-9)(x-1).

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Refer to the attached images.

The volume of prism P is calculated as: 16.55 cm³.

Similar figures are defined as those figures that the same shape, but the sizes are different.

The parameters given are:

- Prism P and prism Q are similar.

- Ratio of the surface area of the prism P to Q = 1 : 3

We also have:

Volume of prism Q = 86 cm³

Scale factor of height of the prism would be square root of surface area of the prism.

Scale factor of volume of the prism would be the cube of the height of the prism.

Let volume of prism P be V(P)

Let the volume of the prism Q be V(Q).

Thus:

V(P) / V(Q) = 1 / (√3)³

V(P) = V(Q) / (√3)³

      = 86 / (√3)³

      = 16.55 cm³

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Answer: Gabriel is 10 years old.

Step-by-step explanation:

Let x represent Gabriel's age and x+2 represent Moussa's age.

x(x+2)=120

x^2+2x=120

x^2+2x-120=0

(Factor quadratic equation): (x-10)(x+12)=0

                                                  x=10, x=-12 --> (age can't be negative)

Gabriel is 10 years old.

The exponential equation that represents the function is 3x².

The finite difference between two consecutive values of f(x) is given by:

Δf(x) = f(x+1) - f(x)

Δf(-6) = f(-5) - f(-6) = 75 - 108 = -33

Δf(-5) = f(-4) - f(-5) = 48 - 75 = -27

Δf(-4) = f(-3) - f(-4) = 27 - 48 = -21

Δf(-3) = f(-2) - f(-3) = 12 - 27 = -15

The second finite differences are:

Δ²f(-6) = Δf(-5) - Δf(-6) = 6

Δ²f(-5) = Δf(-4) - Δf(-5) = 6

Δ²f(-4) = Δf(-3) - Δf(-4) = 6

Since the second finite differences are constant, the function is a quadratic polynomial of the form;

f(x) = ax² + bx + c

f(-6) = 108 = 36a - 6b + c

f(-5) = 75 = 25a - 5b + c

f(-4) = 48 = 16a - 4b + c

The final equation becomes;

36a - 6b + c = 108 ---- (1)

25a - 5b + c = 75 ------ (2)

16a - 4b + c = 48 -------- (3)

solve the equation, using crammers rule,

a = 3, b = 0, c = 0

f(x) = 3x²

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Answer:

The answer for x is 28°

Step-by-step explanation:

x+62=90°

x=90-62

x=28°

I'm rather busy right now but I'll try my best to help you out

1. Radius is 6 because 12/2 = 6

2. Formula is πr^2

im really sry i wasnt able to help out alot but i hope you can understand it a little better

Step-by-step explanation:

its -7.4

because each gap means 0.1

The probability of odds of getting two matching pairs of one type of card, and three matching pairs of another in a hand of five cards are extremely low.

To calculate the odds, we can first calculate the number of ways to get two matching pairs of one type of card, which is (13 choose 2) × (4 choose 2)² since we need to choose 2 ranks out of 13, and then 2 suits out of 4 for each of those ranks. This equals 78,624.

Next, we calculate the number of ways to get three matching pairs of another type of card, which is (11 choose 3) × (4 choose 2)³, since we need to choose 3 ranks out of the remaining 11, and then 2 suits out of 4 for each of those ranks. This equals 15,024. Finally, we multiply the two probabilities to get the overall odds: (78,624 × 15,024) / (52 choose 5) = 0.000016.

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The probability of a student having at least one sibling, based on the survey results is 0.8.

Daniel surveyed 120 students at his school and found that 96 of them have at least one sibling. This means that the probability of a student having at least one sibling, based on the survey results, is 96/120 or 0.8.

There are 425 students at Daniel's school, so if we multiply this number by the probability of having at least one sibling (0.8), we can estimate that approximately 340 students at the school have at least one sibling.

To estimate the number of students at Daniel's school who have at least one sibling, we can use this probability to make a prediction.

If we assume that the probability of a student having at least one sibling is the same for all students at the school, then we can apply this probability to the total number of students.

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The polynomial 2x³ − 5x² + 6x − 15 as a product of binomials is option (a) (x² + 3)(2x − 5).

To factor the polynomial 2x³ − 5x² + 6x − 15 into a product of binomials, we can use the technique of polynomial factorization by grouping.

Factor out the greatest common factor (GCF) from the first two terms and the last two terms separately

2x³ − 5x² + 6x − 15 = x²(2x − 5) + 3(2x − 5)

Notice that we have a common binomial factor of (2x − 5) in both terms. Factor out this common binomial factor

2x³ − 5x² + 6x − 15 = (2x − 5)(x² + 3)

Therefore, the polynomial 2x³ − 5x² + 6x − 15 can be factored as the product of binomials (2x − 5) and (x² + 3).

So, the correct option is (a) (x² + 3)(2x − 5).

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The answers based on the given information:

1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.

2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.

3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.

4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.

5. Since the net investment per worker is negative, capital per worker is decreasing.

7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.

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Answer:

0.14%

Step-by-step explanation:

Answer:

y=-5.3x+36.73

Step-by-step explanation:

The requried, rounding to the nearest gram, mass of the object is 95,297 g.

First, we need to find the volume of the rectangular prism:

Volume = length x width x height = 8 in x 7 in x 5 in = 280 cubic inches

Next, we need to convert the volume to cubic centimeters since the density is given in grams per cubic centimeter:

1 cubic inch = 16.3871 cubic centimeters

280 cubic inches = 280 x 16.3871 = 4594.628 cubic centimeters

Finally, we can calculate the mass of the object using the density formula:

Density = mass/volume

Density x volume

mass = 20.7 g/cm³ x 4594.628 cm³ ≈ 95,296.7 g

Rounding to the nearest gram, the mass of the object is 95,297 g.

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We used a standard deviation to determine whether the bag filling machine was underfilling the bags at the 433 gram setting that is falls within the range of -2.76 to 2.76

To determine whether we should reject or fail to reject the null hypothesis, we will use a hypothesis test with a level of significance of 0.02.

Plugging in the values from the problem, we get:

t = (429 - 433) / (26 / √11)

t = -1.38

To determine whether we should reject or fail to reject the null hypothesis, we will compare the calculated t-value to the critical t-value from the t-distribution table.

Looking up the critical t-value with 10 degrees of freedom and a level of significance of 0.01, we find a value of ±2.76.

Since our calculated t-value of -1.38 falls within the range of -2.76 to 2.76, we fail to reject the null hypothesis.

This means that there is not enough evidence to conclude that the bag filling machine is underfilling the bags at the 433 gram setting.

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Answer:

19%

Step-by-step explanation:

First, find how many water bottles were manufactured in March:

4,100 x 1.07 = 4387

Add 500 to the March number

4387 + 500= 4887

Then divide the April number by February

4887/4100= 1.19195

This means that there is a 19 percent increase of water bottles manufactured from February to April

If baker evenly divides "30" pounds of cookie dough in 7 containers, then each container will contain approximately 4.29 pounds.

To find the amount of cookie dough that the baker will put into each container, we divide the total amount of dough by the number of containers.

The total amount of cookie dough is = 30pounds,

The total number of containers is = 7 containers.

Cookie dough in each container is = 30/7 containers = 4.2857... pounds,

≈ 4.29 pounds,

Therefore, the baker will put approximately 4.29 pounds of cookie dough into each of the 7 containers, if he evenly divides 30 pounds of dough among them.

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Answer & Explanation

Well when we say “ radical form “ just means putting it in square root

“ [tex]\sqrt{}[/tex] “

Square root of 9 is a whole number  since it is not a decimal then it can be multiplied by itself to get the original number. The actual value of square root of 9 is 3. “ √9 = ±3 “

If we square root +3 or -3, the resulting value will be equal to 9. Shown:

[tex](+3)^{2} = 9[/tex]

[tex](-3)^2 = 9[/tex]

Does not matter any order.

The probability that a randomly selected marble is purple or small is: 0.5254

The total number of big marbles = 34 marbles

The total number of small marbles = 25 marbles

The total number of red marbles = 22 marbles

The total number of Green Marbles = 11 marbles

The total number of purple marbles = 16 marbles

The total number of blue marbles = 10 marbles

Total number of all marbles = 59 marbles

Thus, the probability that a randomly selected marble is purple or small is:

P(purple or small) = (16/59) + (25/59)

= 31/59 = 0.5254

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Answer:

20/100=0.20

0.20$(58) +$58

option A

The amount of wrapping paper for the gift is A = 279 inches²

Given data ,

To calculate the amount of wrapping paper Laura will need to wrap the gift, we need to find the total surface area of the gift.

The surface area of a rectangular box is given by the formula:

Surface Area = 2 x (length x width + length x height + width x height)

Given that the length of the gift is 6 inches, the width is 13.5 inches, and the height is 3 inches, we can substitute these values into the formula:

Surface Area = 2 x (6 x 13.5 + 6 x 3 + 13.5 x 3)

Surface Area = 2 x (81 + 18 + 40.5)

Surface Area = 2 x 139.5

The surface area of a rectangular box = 279 inches²

Hence , Laura will need 279 inches² of wrapping paper to wrap the gift

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To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we substituted -3 for y and simplified. The first expression evaluates to 2, and the second evaluates to approximately -17.333.

To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we can simply substitute -3 for y in each expression and simplify

2(y+6)/3 = 2(-3+6)/3

Now, simplifying by simple subtraction and then multiply,

= 2(3)/3 = 6/3 = 2

Therefore, when y=-3, the value of 2(y+6)/3 is 2.

Now, substituting the value of y =-3

(4y+64)/(-3) = (4(-3)+64)/(-3) = (-12+64)/(-3) = 52/(-3) = -17.333...

Therefore, when y=-3, the value of (4y+64)/(-3) is approximately -17.333.

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The price at which the company should sell its phones to get the maximum revenue is $250

Attaining peak yields is the preeminent rate of profits that a commerce or congregation can accumulate from its action, products, or amenities within a determined span.

It is where the firm or collective is accruing the most money achievable, harnessing its present facilities, marketplace appeal, pricing methods, along with other specifics.

In order to attain maximum revenue, an enterprise must focus on refining its sales and networking campaigns, developing its wares or services, determining and honing in on precise shoppers, and optimizing its expenses as well as costs efficaciously.

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The volume of the orange traffic cones is 102.63 in³ respectively.

A cone is a recognizable three-dimensional geometric shape with a smooth and curving surface that is directed upward in mathematics. The

Greek word "konos," which denotes a peak or a wedge, is the source of the English word "cone."

The apex is the pointy end, while the base is the level area.

So, the cone volume is:

V=πr²h/3

Now, insert values as follows:

V=πr²h/3

V=π7²2/3

V=102.63

Therefore, the volume of the orange traffic cones is 102.63 in³ respectively.

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The sum of horizontal forces acting on a body in equilibrium must be zero.

(a) 12 N + 24 N + 48 N = 84 N ≠ 0, so not in equilibrium.

(b) 50 N + 75 N + 150 N = 275 N ≠ 0, so not in equilibrium.

(c) 45 N + 90 N + 450 N = 585 N ≠ 0, so not in equilibrium.

(d) 35 N + 35 N + 35 N = 105 N = 0, so this set of forces can keep a body in equilibrium.

Therefore, the correct answer is (d) 35 N, 35 N, and 35 N.

Answer:

6,3,7

Step-by-step explanation:

this is because they are all obtuse angles please help me i have a brain fart on meidan  of 45, 52, 57, 42, 54, 58.