(c) Problem 17:
How far will the baseball have dropped after
4.5 seconds?
(first taught in
lesson 90)
Afton

Answer:

False

Step-by-step explanation:

This is because runner 1's median line falls on 5.6-5.7s while runner 2's falls on 6.4s

(Hopes this helps :) )

Angle Y from the given triangle XYZ is 62° and sine of ∠Y is 60/68.

From the given triangle XYZ, XY=32 and YZ=68.

By using Pythagoras theorem, we get

YZ²=XY²+XZ²

68²=32²+XZ²

XZ²=68²-32²

XZ²=3600

XZ=√3600

XZ=60

We know that, sinθ= Opposite/Hypotenuse

sinY=XZ/YZ

sinY=60/68

sinY=0.8823

Y=61.92

Y≈62°

Therefore, angle Y from the given triangle XYZ is 62° and sine of ∠Y is 60/68.

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Answer: What are we finding?

Step-by-step explanation:

To solve the equation for C, first factor out the common monomial C, then rewrite the equation as C(1 + 0.20) = T.

Then, to isolate the variable, divide both sides by the factor (1 + 0.20) or 1.20: C = T/1.20.

An equation is essentially a statement that illustrates the variables presented. In this circumstance, it is critical to notice that two or more components are taken into account in order to represent the scenario.

Based on the information, to solve the equation for C, first factor out the common monomial C to rewrite the equation as C(1 + 0.20) = T.

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The equation of the trend line in slope intercept form is: K = -2J + 28

The formula for the equation of a line in slope intercept form is expressed in the form:

y = mx + c

where:

m is slope

c is y-intercept

Now, from the given line of best fit, we see that:

At x = 0, y = 28

Thus, c = 28

To get the slope, we will take 2 coordinate points which are:

(2, 24) and (4, 20)

Thus:

m = (20 - 24)/(4 - 2)

m = -2

Thus, the equation is:

K = -2J + 28

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The probability of getting a 6 on a biased dice is 0.4. The P(X ≤ 2) is 0.936.

The probability of rolling a 6 is 0.4 and the probability of not rolling a 6 is 0.6. The probability mass function for X is given in the table. To find P(X ≤ 2), we need to sum the probabilities for X = 0, 1, and 2.

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.216 + 0.432 + 0.288

= 0.936

Therefore, the probability of rolling a 6 two or fewer times in three trials is 0.936 (rounded to 3 decimal places).

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Answer:0.432

Step-by-step explanation:

edge

The measure of the angle S is 54 degrees

Using the Pythagorean theorem, we have that;

r² = t² + s²

Subsitute the values

s² = 24² - 14²

Find the square values

s² = 576 - 196

s² = 380

find the square root value

s = 19. 5

Then, using the law of sines, we have that;

sin R/r = sin S/s

Substitute the values, we get;

sin 98/24 = sin S/19.5

cross multiply the values

sin S = 19.3/24

Divide the values

sin S = 0. 8045

S = 54 degrees

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The characteristics of the quadratic function and its graph are listed below

From the question, we have the following parameters that can be used in our computation:

The graph of the quadratic function

As a general rule

The domain of a quadratic function is the set of all real values

For the range, we have

The graph has a maximum value at y = -1

Also, the values of the function output (y values) decreases

This means that the range is y <= -1

For other key features, we have

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The calculated value of the  length of the arc JK is 35π/12

From the question, we have the following parameters that can be used in our computation:

central angle = 75 degrees

Radius = 7

Using the above as a guide, we have the following:

Arc JK = central angle/360 * 2 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

JK = 75/360 * 2 * π * 7

Evaluate

JK = 35π/12

Hence, the length of the arc JK is 35π/12

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Complete question

Find the indicated measure. Length of JK

See attachment

The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).

Given expression is,

[15 / (x - 6)] + [7 / (x + 6)]

Cross multiplying the two fractional expressions,

= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]

= [15x + 90 + 7x - 42] / [x² - 6²]

= (22x + 48) / (x² - 36)

Hence the equivalent expression is D.

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The polynomial function of least degree with integer coefficients is: P(x) = a(x³ + 14x² - 31x + 16)

Given that the properties of the polynomial are

If a polynomial has the given zeros 1 with a multiplicity of 2 and another zero at 4i, then its factors can be written as:

P(x) = a(x - 1)²(x - 4i)(x + 4i)

Multiplying out these factors, we get:

P(x) = a(x - 1)²(x + 16)

Expanding the right-hand side, we get:

P(x) = a(x³ + 14x² - 31x + 16)

Therefore, the polynomial function is: P(x) = a(x³ + 14x² - 31x + 16)

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The volume of one salt lick is 125/1728 feet which is less than one cubic foot.

All the edges of the cube are congruent with each other. Suppose that: The side length of the considered cube is L units. Then, we get:

V = L³ cubic units.

The edge length of the cube is 5/12 feet. Then the volume of the cube will be given as,

V = (5/12)²

V = 125 / 1728 feet

The volume is less than one cubic foot.

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Answer:

[tex] \frac{\pi( {4}^{2}) }{\pi( {8}^{2}) } = \frac{16}{64} = \frac{1}{4} = .25[/tex]

If  u = - 3i + 2i,  v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.

To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:

3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j

Next, we can perform the scalar multiplication of u and the vector 6i + 14j:

5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)

Expanding the product, we get:

5(-18i² + 36ij + 42ij - 28j²)

Since i² = j² = -1, we can simplify this expression as:

5(18 + 70) = 440

Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.

The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.

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The possible values lx + 5| = 6 of x in the equation are x = -11 or x = 1

From the question, we have the following parameters that can be used in our computation:

lx + 5= 6

Express properly

So, we have

lx + 5| = 6

The above equation is an absolute value equation

When the above equation is expanded, we abe

x + 5 = -6 or x + 5 = 6

Solving for x in the equations. we have

x = -11 or x = 1

This means that the values of x in the equation are x = -11 or x = 1

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The equation in each case will be 5(x - 2) = x + 7, 2x - 4 > 10, and 2x - 2 = x + 5 and their solution will be 4.25, more than 7, and 7, respectively.

1. Let the number be x. Then the equation can be written as,

5(x - 2) = x + 7

5x - 10 = x + 7

4x = 17

x = 4.25

2. Let the number be x. Then the equation can be written as,

2x - 4 > 10

2x > 14

x > 7

3. Let the number be x. Then the equation can be written as,

2x - 2 = x + 5

x = 7

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Answer:

25 miles

Step-by-step explanation:

Robert runs 7 1/5 miles on Saturday. To find out how much he runs on Monday and Wednesday, we can multiply 7 1/5 by 2:

7 1/5 x 2 = 14 2/5

Robert runs 14 2/5 miles on both Monday and Wednesday, so his total distance for the week is:

7 1/5 + 14 2/5 + 14 2/5 = 35 miles

Robert wants to run a total of 60 miles this week, so he needs to run:

60 - 35 = 25 miles

Therefore, Robert needs to run 25 more miles to reach his goal of running 60 miles this week.

Answer:

To solve for y in the equation:

3y - 1/3 = 5

First, we need to isolate the term containing y by adding 1/3 to both sides of the equation:

3y - 1/3 + 1/3 = 5 + 1/3

Simplifying the left-hand side:

3y = 5 + 1/3

Next, we need to isolate y by dividing both sides of the equation by 3:

3y/3 = (5 + 1/3)/3

Simplifying the right-hand side by finding a common denominator:

3y/3 = (15/3 + 1/3)/3

3y/3 = 16/3

Simplifying the left-hand side:

y = 16/9

Therefore, the solution to the equation 3y - 1/3 = 5 is y = 16/9.

Step-by-step explanation:

The solution is,  the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water is

y-29 = -7/2 (x-6).

Here, we have,

The given data is

time (h):    2   4   6   8

gallons:  43 36 29 22

A graph of the data shows a linear relationship.

Therefore in slope-intercept form, let

(y - 29)/(x - 6) = m

where m = the slope of the straight line.

Calculate the slope.

m = (43 - 22)/(2 - 8) = -7/2

Answer:  y-29 = -7/2 (x-6)

Hence, The solution is,  the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water is

y-29 = -7/2 (x-6).

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Answer:

5(-6 + 2n) can be simplified using the distributive property of multiplication as follows:

5(-6 + 2n) = 5*(-6) + 5*(2n)

= -30 + 10n

Therefore, the simplified expression is -30 + 10n.

Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.

(1)

(a) The relationship between D, o, and S can be expressed as follows:

DoS (D divided by o multiplied by S) = D / (35 * S)

(b) To find the value of S when D is 176, we can substitute D = 176 into the equation from part (a):

DoS = 176 / (35 * S)

Since the relationship between DoS is not specified further, we cannot determine a specific value of S without additional information. We need more context or a specific equation to solve for the value of S.

Let's denote the amount Alfa gets as x Naira. According to the given information, Aisha gets twice as much as Alfa, so Aisha receives 2x Naira.

The sum of the amounts they receive is 210 Naira, so we can set up the equation:

x + 2x = 210

Combining like terms:

3x = 210

Dividing both sides by 3:

x = 70

Therefore, Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.

In summary, Alfa receives 70 Naira, while Aisha receives 140 Naira.

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The surface area of the rectangular prism is 216 square inches

From the question, we have the following parameters that can be used in our computation:

10 in by 3 in by 6 in

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)

Evaluate

Area = 216

Hence, the area is 216 square inches

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The ratio of boys to girls in Mrs. Franco's class is 3:2 .

Here, we have,

The Ratio is defined as the comparison of two quantities that have the same units .

In the question ,

it is given that

In Mrs. Franco's class

For every 6 boys there are 4 girls in the class

we have to find the ratio of , boys to girls

the number of boys = 6

the number of girls = 4

So , the ratio can be written as

boys / girls = 6/4

writing the ratio in the simplest form , we get

boys/girls = 3/2

the ratio is 3:2   .

Therefore , The ratio of boys to girls in Mrs. Franco's class is 3:2 .

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complete question:

In Mrs. Franco‘s class for every 64 is there a April right the ratio of boys to girls in simplest form

The sale prices of the four items are Coat: $111.99, Blouse: $35.19, Shoes: $71.99, Jeans: $26.39 , Using the discount percentage and Using the discount amount are two different ways to find the sale prices.

To find the sale price of each item, we need to multiply the regular price by the discount percentage, which is 20% or 0.2.

Then we subtract this discount amount from the regular price to get the sale price. We can use the following formula:

Sale price = Regular price - Discount amount

Using this formula, we can calculate the sale prices of the four items:

Coat: Sale price = $139.99 - ($139.99 x 0.2) = $111.99

Blouse: Sale price = $43.99 - ($43.99 x 0.2) = $35.19

Shoes: Sale price = $89.99 - ($89.99 x 0.2) = $71.99

Jeans: Sale price = $32.99 - ($32.99 x 0.2) = $26.39

Therefore, the sale prices of the four items are:

Coat: $111.99, Blouse: $35.19, Shoes: $71.99, Jeans: $26.39.

b. There are different ways to find the sale prices. Here are two methods:

Method 1: Using the discount percentage

Multiply the regular price of each item by the discount percentage (20% or 0.2).

Subtract the result from step 1 from the regular price to find the sale price.

Method 2: Using the discount amount

Multiply the regular price of each item by the discount percentage (20% or 0.2) to find the discount amount.

Subtract the discount amount from the regular price to find the sale price.

Both methods will give you the same sale prices, but some people may find one method easier or more intuitive than the other.

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The overall probability of drawing B-R-A-D in that order is 1/24.

Option C is the correct answer.

We have,

The probability of drawing the letters B-R-A-D in that order is equal to the product of the probabilities of drawing each letter in that order.

Since we are drawing without replacement, the probability of drawing the first letter B is 1/4.

Then, the probability of drawing the second letter R is 1/3

(since one letter has already been drawn and removed from the hat).

Similarly, the probability of drawing the third letter A is 1/2 and the probability of drawing the fourth letter D is 1/1

(since all the other letters have already been drawn and removed).

The overall probability of drawing B-R-A-D in that order.

= (1/4) x (1/3) x (1/2) x (1/1)

= 1/24

Thus,

The overall probability of drawing B-R-A-D in that order is 1/24.

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The requried position of point B on the number line is 1/4 or 0.25.

Since point B represents the number 0.25 on the number line, its position can be described as 0.25 units to the right of 0 or as 0.25 units to the left of 0.5.

Alternatively, we can describe its position as a fraction or mixed number using the length of the number line as the denominator. If the number line extends from 0 to 1, then the position of point B can be expressed as:

B = 0 + 0.25 = 1/4

Therefore, the position of point B on the number line is 1/4 or 0.25.

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If the linear equation 2x+3y=14 is rewritten in function notation as f(y)=−32y+7, the dependent variable is x

In the linear equation 2x+3y=14, we can solve for y by isolating it on one side of the equation:

2x + 3y = 14

3y = -2x + 14

y = (-2/3)x + 14/3

Now, we can write this equation in function notation by replacing y with f(y) and x with the independent variable, usually denoted by 'x'. Therefore, we have:

f(y) = (-2/3)x + 14/3

The function f(y) tells us the value of x for any given value of y. In other words, y is the independent variable, and x is the dependent variable.

Therefore, the dependent variable in the function f(y) = (-2/3)x + 14/3 is x. The value of x is determined by the value of y, which is the input to the function. This means that for any value of y, we can determine the corresponding value of x by plugging in y into the equation and solving for x.

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Answer:

4 months

Step-by-step explanation:

This question is just asking you to construct a system of equations!

The amount that they will start with will be the y-intercept, because that's the amount in the bank account when no time has passed (aka since no additional deposits were made).

Chrisitiana: 10x + 50 = y

Marlena: 15x + 30 = y

Y in this case is going to be the amount of money in the bank account when x amount of months have passed. We want both y values to be the same.

10x + 50 = y = 15x + 30

Cut out the y as a middleman and we have

10x + 50 = 15x + 30

-10x

50 = 5x + 30

-30

20 = 5x

/5

4 = x

They will have the same amount of money in their accounts after 4 months.