What is the probability that the total team time in the
400-meter freestyle relay is less than 215 seconds?
O 0.056
O 0.1665
O 0.8335
0.944

Answer:

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

When t = 0, the velocity is:

[tex]\begin{aligned}\vec{v}(t)&=3^t \vec{i}+e^{6t} \vec{j}\\\\t=0 \implies \vec{v}(0)&=3^0 \vec{i}+e^{(6 \cdot 0)} \vec{j}\\ &=1 \vec{i}+1 \vec{j} \end{aligned}[/tex]

Speed is the magnitude of the velocity of the object.

[tex]\boxed{\text{A vector $\binom{x}{y}$ has magnitude $\sqrt{x^2+y^2}$}}[/tex]

Therefore, the particle's speed at time t = 0 is:

[tex]\begin{aligned}\implies |v|&=\sqrt{1^2+1^2}\\&=\sqrt{1+1}\\&=\sqrt{2}\end{aligned}[/tex]

The distance from the point A to point B is s√3

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

Perfect cube with sides of length s.

The distance from point A to point B is calculated as

Distance^2 = s^2 + s^2 + s^2

When evaluated, we have

Distance^2 = 3s^2

Take the square roots of both sides

Distance = s√3

Hence, the distance = s√3

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Answer:

The three numbers are -4, 0, and 1.

Step-by-step explanation:

mark brainliest

Answer:

n=-4

Step-by-step explanation:

5(3n+4n+3) = -125

First, combine like terms:

5(7n+3) = -125

Then, distribute the 5:

35n+15 = -125

Then, get n by itself:

35n= -140

Then, divide by 35 to get n by itself:

n = -140/35

Simplify

n = -4

The solution to the system of equations in this problem is given as follows:

(-1, -5).

The system of equations in the context of this problem is defined as follows:

The x-coordinate of the solution in the context of this problem is obtained equaling the two equations, as follows:

x - 4 = -3x - 8

4x = -4

x = -1.

Hence the y-coordinate of the solution is obtained as follows:

y = -1 - 4

y = -5.

Thus the solution is:

(-1, -5).

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Answer:

1. 69.73 is the Area of the Rectangle. 50.27 is the Area of the Circle. 2. 120 is the area of the parallelogram, 25.13 is the area of the semi-circle

Step-by-step explanation:

For #1, We can to 15 * 8 to get area of what would be the whole rectangle. It is 120. Then, calculate area of the circle, pi * 4^2(4 because the 8 is a diameter. That totals to 50.27 for the circle. Subtract the two, 120-50.27 and you get 69.73 as the area of the shape excluding the circular portion.

For #2, We can apply the same formula for the circle, and divide it by two this time for 25.13 as the circle area. We can use the paralellogram formula of b*h (6*20) and we get 120 for that area. The total for the whole figure on #2 is 145.13 square units.

Note: unit for both is square units, as it is not specified.

An exponential model for the number of SMS messages sent annually for years before 2012 is [tex]y = 12421e^{0.2325x}[/tex].

In this scenario, the year would be plotted on the x-axis (x-coordinate) of the scatter plot while the SMS messages would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the year and SMS messages, an exponential equation for the line of best fit is given by

[tex]y = 12421e^{0.2325x}[/tex]

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The possible combinations of hand pies and gourmet cupcakes that the baker could sell for exactly $45.00 are:

The possible combinations of hand pies and gourmet cupcakes can be determined by finding the results of each combination using multiplication and addition.

Multiplication and addition are two of the four basic mathematical operations, including division and subtraction.

The unit cost of hand pies = $5

The unit cost of cupcakes = $3

The total sales revenue = $45

a. No hand pies and 15 gourmet cupcakes = $45 ($5 X 0 + $3 x 15)

b. 2 hand pies and 11 gourmet cupcakes = $43 ($5 X 2 + $3 x 11)

c. 3 hand pies and 10 gourmet cupcakes = $45 ($5 X 3 + $3 x 10)

d. 5 hand pies and 6 gourmet cupcakes = $43 ($5 X 5 + $3 x 6)

e. 6 hand pies and 5 gourmet cupcakes = $45 ($5 X 6 + $3 x 5)

f. 8 hand pies and 2 gourmet cupcakes = $46 ($5 X 8 + $3 x 2)

g. 9 hand pies and no gourmet cupcakes = $45 ($5 X 9 + $3 x 0)

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The half-life of this radioactive element is approximately 2 years.

We have,

The decay of a radioactive element follows an exponential decay model of the form:

[tex]N = N_0 e^{-kt}[/tex]

where:

N0 is the initial concentration of the radioactive element

N is the concentration after time t

k is the decay constant

We are given that the element has decayed to 1/32 of its original concentration, which means that its current concentration is 1/32 times its initial concentration:

N/N0 = 1/32

Taking the natural logarithm of both sides and rearranging, we get:

ln(N/N0) = ln(1/32) = -3.465

Now we can use the formula for half-life, which relates the decay constant to the half-life t1/2:

t1/2 = ln(2) / k

We can solve for the decay constant k by using the information that the element has decayed to 1/32 of its original concentration in 10 years:

ln(N/N0) = -kt

-3.465 = -k x 10

k = 0.3465

Substituting this value of k into the formula for half-life, we get:

t1/2 = ln(2) / k = ln(2) / 0.3465 = 2.0 x 10^0 years = 2 years.

Therefore,

The half-life of this radioactive element is approximately 2 years.

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Answer:

12.28

Step-by-step explanation:

To solve this problem you have to spilt the problem into 2 parts.

First, let us solve the triangle.

The formula to find the area of a triangle is [tex]\frac{1}{2}bh[/tex]. The base of this triangle is 3 and the height is 4. This leaves us with an answer of 12. The next step is to divide 12 by two. So now we have the area of the triangle as [tex]6 km^2[/tex].

Second, let's solve the hemisphere.

The formula to find the area of a circle is [tex]\pi r^{2}[/tex]. Because this is a hemisphere we can divide the formula by two to get [tex]\frac{\pi r^2}{2}[/tex]. Now let us insert the values.

In this problem, we have the diameter of the semicircle. To find the radius we divide the diameter by two. This gives us a radius of 2km.

The next step is to multiply 3.14 * 2^2 and divide this by 2:

[tex]\frac{\pi 2^{2} }{2}[/tex]

[tex]\frac{\pi 4}{2}[/tex]

[tex]\frac{12.56}{2}[/tex]

[tex]6.28[/tex]

Lastly, our final step is to add both the triangle area and the area of the semicircle.

[tex]6+6.28[/tex]

[tex]12.28[/tex]

12.28 is our final answer.

Answer: 2x + 12

Step-by-step explanation:

Let the cost of each sweater be x.

since she's buying 2, the total cost of the sweaters will be 2x.

Just tack on the + 12 at the end for the sunglasses :)

The confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)

Solve for the sample proportion

= 602/1000 = 0.602

z* is the critical value from the standard normal distribution at the 95% confidence level = (1.96)

n =  sample size (1000)

CI = 0.602 ± 1.96√((0.602(1-0.602))/1000)

CI = 0.602 ± 0.032

0.602 - 0.032 , 0.602 + 0.032

CI = (0.57, 0.63)

Hence the confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)

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The slope represents that: a Fahrenheit degree change is equivalent to a Celsius change of 2 degrees.

The y-intercept of 32 represents that: It is the melting point of water on the Fahrenheit scale.

The general form of expression of Linear functions in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Now, the equation is given as:

F = 2C + 32

Thus:

Slope = 2

y-intercept = 32

The slope is 2. This means that a Fahrenheit degree change is equivalent to a Celsius change of 2 degrees.

The y-intercept is 32. This is the melting point of water on the Fahrenheit scale.

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There is a remarkable discrepancy in perceived organization support amongst female and male employees: women garnered a superior mean score (M=4.65, SD=0.58) as opposed to males (M=4.42, SD=0.70), t(198)=2.51, p<0.05.

Consequently, we recommend that the committee delve into the source of this divide and take steps to ensure that both sexes receive the same level of solidarity.

It was established that there was no distinct disparity in distributive justice perceptions between female and male employees: females earned a mean score of 4.16 (SD=0.64), while men attained a mean score of 4.14 (SD=0.61), t(198)=0.23, p>0.05.

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The number of ways of selecting 3 items from a total of 7 items, where order does not matter is (a) 35 ways.

The number of ways to choose three items from a group of seven, where order does not matter, is given by the combination formula:

⇒ C(n,r) = n!/(r! × (n-r)!),

where n is = total number of items, and r is = number of items to be chosen,

We have, total items (n) = 7 and items to be selected (r) = 3.

Substituting the values,

We get;

⇒ C(7,3) = 7!/(3! × (7-3)!),

⇒ 7!/(3! × 4!),

⇒ (7 × 6 × 5)/(3 × 2 × 1),

⇒ 35 ways.

Therefore, the correct option is (a).

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Answer:

17.

90 - 75 = 15

Answer: b

18.

ABC

Answer: A

19.

Answer: D

20.

Answer: D

The measure of angle 3 is 52⁰.

The measure of angle 5 is 38⁰.

The measure of angle 6 is 52⁰.

The measure of angle 3, 5 and 6 is calculated as follows;

angle 1 + angle 2 + angle 3 = 180 (sum of angles in straight line )

90 + 38 + angle 3 = 180

angle 3 = 180 - 128

angle 3 = 52⁰

The measure of angle 5 is calculated as follows;

angle 5 = angle 2 (vertical opposite angles are equal)

angle 5 = 38⁰

The measure of angle 6 is calculated as follows;

angle 6 = angle 3 (vertical opposite angles are equal)

angle 6 = 52⁰

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As per the given details, the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

To rewrite the equation y+5=5(x-4) in Ax+By=C form, we need to simplify and rearrange the equation to isolate y on one side:

y + 5 = 5(x - 4)

y + 5 = 5x - 20 (Distribute 5 on the right side)

y = 5x - 20 - 5 (Subtract 5 from both sides)

y = 5x - 25

Now the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To rewrite it in Ax + By = C form, we need to rearrange the terms to get the x and y terms on the left side and a constant on the right side:

y = 5x - 25

-5x + y = -25

So the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

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Answer:

1 inch

Step-by-step explanation:

Answer:

V = 62.8 m[tex]^{3}[/tex]

Step-by-step explanation:

V = pi × (radius)[tex]^{2}[/tex] × height

V = [tex]\pi[/tex] × [tex]r^{2}[/tex] × h

V = (3.14 × [[tex]2^{2}[/tex]]) × 5

V = (3.14 × 4) × 5

V = 12.56 × 5

V = 62.8 m[tex]^{3}[/tex]

Answer: 20

Step-by-step explanation:

because Juanita has a aquarium that is 5 feet LONG, 4 feet WIDE, and 2 feet DEEP, in part b it asks what if the water is 1 foot DEEP so what they're trying to say is what if you replace the original 2 feet DEEP with 1 foot DEEP?

so it would be length x width x depth

5x4x1=20

so the volume is 20ft^3

The amount of money that Nora would need to invest is $25913.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

[tex]72,000 = P(1 + \frac{0.064}{365})^{365 \times 16}\\\\72,000 = P(1 + 1.75 \times 10^{-4})^{5,840}\\\\72,000 = P(1.000175)^{5,840}[/tex]

P = 72,000/2.77849825425152

Principal, P = $25913.28 ≈ $25913

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A relation represents a function when each input value is mapped to a single output value.

On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.

Tracing a vertical line for any x > -3, the vertical line would cross the graph at two points, meaning that the relation is not a function.

As for the domain and the range, we have that:

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Answer:

192pie

Step-by-step explanation:

To find the area of a circle, it is pie (3.14) times r². The radius is 24, so it is 24² times pie. The area is 576 pie. Now to find the area of the shaded, you would do 1/3 times the area. 1/3 of 576 is 192. The answer is 192pie

If the "angle M" measures 98° and "angle N" measures (6x + 2)°, then value of "x" must be 16.

When the "two lines" intersect, the opposite angles formed are equal in measure, which means that vertical angles are congruent. So, we have:

⇒ Angle M = Angle N

Using the given values, we can write an equation:

⇒ Angle M = 98°  and Angle N = (6x + 2)°,

Setting them equal,

We get,

⇒ 98 = 6x + 2,

Solving for x, we subtract 2 from both sides and then divide by 6:

⇒ 96 = 6x,

⇒ x = 16,

Therefore, the variable "x" must be 16 for "angle N" to be vertical to "angle M".

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The given question is incomplete, the complete question is

If an "angle N" is vertical to "angle M", and measure of "angle M" is 98° and the measure of angle N is (6x + 2)°, the x must be.

b) By basing on the findings in part (a), we rejected the null hypothesis. This implies that a Type I error – which is the mistake of disregarding a validly-true null supposition – could have potentially been made.

(c) Since the confidence interval holds both negative and positive values, we are not able to confirm that leastwise some dissimilarity might exist between these two proportions.

d) Raising the power of the test may be achievable by lessening the significance level.

In this state, it would indicate that we concluded that there exists a considerable divergence between the proportion of men and women intending to vote for Trump when factually there is no distinction.

Raising the power of the test may be achievable by lessening the significance level. Doing so will penalize us with being more lenient towards taking up the alternate assumption, consequently reducing the likelihood of having a Type II error.

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Answer: b=18.1 and c=14.3

Step-by-step explanation:o solve for the lengths of the sides b and c in triangle ABC, we can use the law of sines, which relates the lengths of the sides of a triangle to the sines of the angles opposite those sides. Specifically, the law of sines states that:

a/sin(A) = b/sin(B) = c/sin(C)

where A, B, and C are the angles of the triangle opposite sides a, b, and c, respectively.

Given that a = 17, B = 70°, and C = 48°, we can write:

b/sin(70°) = 17/sin(A)

c/sin(48°) = 17/sin(A)

To solve for b and c, we need to find sin(A). We can do this by using the fact that the angles of a triangle sum to 180°:

A + B + C = 180°

A = 180° - B - C

A = 180° - 70° - 48°

A = 62°

Now we can substitute sin(A) = sin(62°) into the equations above and solve for b and c: