What is the measure of the other acute angle

Answer:

XY = 9

Step-by-step explanation:

Similar polygons have corresponding sides with proportional lengths.

WX/AB = XY/BC

12/8 = XY/6

8XY = 12 * 6

8XY = 72

XY = 9

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : [tex]$h(x)=x^2-7x+6$[/tex]

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

[tex]$h(0)=0^2-7(0)+6$[/tex]

       [tex]$=0-0+6$[/tex]

       [tex]$=6$[/tex]

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

   It is the minimum height which represents the depth Kendra dives into the water.

So the [tex]$x$[/tex] coordinate of the vertex is = [tex]$\frac{-b}{2a}$[/tex]

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴  x coordinate = [tex]$\frac{-(-7)}{2 \times 1} $[/tex]

                         [tex]$\frac{7}{2}=3.5$[/tex]

Now substituting to find f(x),

[tex]$h(3.5)=(3.5)^2-7(3.5)+6$[/tex]

         = -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ [tex]$0=x^2-7x+6$[/tex]

Factorizing, we get   [tex]$(x-1)(x-6)=0$[/tex]

∴ [tex]$x=1 \text{ or}\ x=6$[/tex]

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has [tex]$\text{two}$[/tex] x intercepts. These two x intercepts  are the points where the parabola crosses the x-axis, which is the height [tex]$h(x)=0$[/tex]. The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is [tex]$x=6$[/tex] for [tex]$h(x)=0$[/tex].

Thus Kendra dives out of the water surface at 6 feet from the board.

The set in problem 8 was not a subspace because one of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom

a. The set F is a subset of the vector space of continuous functions on some interval, which we have studied this semester.

b. To prove whether F is a subspace of the vector space of continuous functions, we need to check if F satisfies the three subspace axioms: closure under addition, closure under scalar multiplication, and the zero vector property.

Let f and g be two functions in F, and let c be a scalar. To show closure under addition, we need to prove that f + g is also in F. Since both f and g have the property that f'(2) = 0 and g'(2) = 0, their sum (f + g) will also have the property that (f + g)'(2) = f'(2) + g'(2) = 0 + 0 = 0. Therefore, f + g is in F.

To show closure under scalar multiplication, we need to prove that cf is also in F. Again, since f has the property that f'(2) = 0, multiplying f by any scalar c will not change the derivative at 2. Therefore, (cf)'(2) = c × f'(2) = c × 0 = 0, and cf is in F.

Finally, the zero vector property states that the zero function, denoted as 0, must be in F. The zero function has the property that its derivative is always zero, including at 2. Therefore, 0'(2) = 0, and the zero function is in F.

Since F satisfies all three subspace axioms, we can conclude that F is a subspace of the vector space of continuous functions.

c. We can get away with not checking the other eight axioms (associativity, commutativity, distributivity, etc.) because F is a subset of a known vector space. By being a subset of a vector space, F inherits those axioms from the larger vector space. The other eight axioms are properties of vector spaces that hold true for all vectors in the larger vector space, including the vectors in F. Therefore, if F satisfies the subspace axioms, it automatically satisfies the other eight axioms by virtue of being a subset of a vector space.

d. It was not okay to only check the two subspace axioms on problem 8 from exam 2 because the set in that problem did not satisfy the zero vector property. One of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom. As a result, the set in problem 8 was not a subspace.

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To find the division of z1 by z2 in polar form, where the angles are given in degrees, we have z1 = 15 cis (83°) and z2 = 6 cis (114°). The polar form of the division of z1 by z2 is 2.5 cis (329°).

To divide complex numbers in polar form, we can divide their magnitudes and subtract their angles. Let's start by dividing the magnitudes:

|z1/z2| = |z1|/|z2| = 15/6 = 2.5

Next, we subtract the angles:

θ = θ1 - θ2 = 83° - 114° = -31°

Since the angle is negative, we add 360° to it to get a positive angle in the standard range:

θ = -31° + 360° = 329°

Therefore, the division of z1 by z2 in polar form is given by:

z1/z2 = 2.5 cis (329°)

So, the polar form of the division of z1 by z2 is 2.5 cis (329°).

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Answer:

1/3, 1/2, 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

(5,3) should be your slope. Start from the bottom of the line and go up. Use the X axis slope 1st because of the x1 y1 coordinates.

Answer:

(5,-1)

(-4,0)

Step-by-step explanation:

5 is in the X axis

-1 is in the Y axis

-4 is in the Y axis

0 is in the X axis

Answer:

First answer choice

Step-by-step explanation:

Answer:

The answer would be A

Step-by-step explanation:

To test the hypothesis of mean differences in artificially sweetened drink consumption among BMI groups, assuming a normal distribution, the researcher might use a one-way ANOVA.

The one-way ANOVA compares the means of three or more independent groups and determines if there are statistically significant differences among them. In this case, the BMI groups (normal weight, overweight, and obese) represent the independent groups, and the number of artificially sweetened drinks consumed is the dependent variable. By conducting a one-way ANOVA, the researcher can assess if there are significant differences in mean consumption among the BMI groups and draw conclusions regarding their hypothesis.

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Answer:

[tex]y = 3x - 0.5[/tex]

Step-by-step explanation:

Given

Goes through

[tex]C = (1.5,4)[/tex]

Parallel to AB

[tex]A = (2,-1)[/tex]

[tex]B = (4,5)[/tex]

Required

Determine the line equation

First, calculate the slope of AB

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{5--1}{4-2}[/tex]

[tex]m = \frac{6}{2}[/tex]

[tex]m = 3[/tex]

The line is said to be parallel to AB. This implies that their slopes are equal.

The equation of the line is then calculated as:

[tex]y = m(x - x_1) + y_2[/tex]

Where:

[tex](x_1,y_1) = (1.5,4)[/tex]

So:

[tex]y = 3*(x - 1.5) + 4[/tex]

[tex]y = 3x - 4.5 + 4[/tex]

[tex]y = 3x - 0.5[/tex]

The null distribution used for a hypothesis test of a single population proportion is the standard normal distribution. The correct answer is b).

When conducting a hypothesis test for a single population proportion, we use the standard normal distribution as the null distribution. This is based on the assumption that the sampling distribution of the sample proportion follows a normal distribution when the sample size is sufficiently large.

The hypothesis test for a single population proportion involves comparing the observed sample proportion to the hypothesized population proportion. We calculate the test statistic, which is the standard error of the sample proportion under the null hypothesis, divided by its standard deviation.

Since the test statistic follows a normal distribution under the null hypothesis, we compare it to critical values from the standard normal distribution to determine the p-value and make a decision regarding the null hypothesis.

Therefore, correct option is B.

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Answer:

9 [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Answer:

I believe the simplified form of this ratio is 1:3

*The common factor to both numbers is 27.

27÷27=1 and 81÷27=3

So, that's where the 1:3 came from

If The results of the study reveal that n=40, sample mean = $16,000, and sample standard deviation = $5,000 then the probability is about 65.54%.

To calculate the probability that a randomly selected recent graduate has savings of $18,000 or more, we first need to calculate the z-score using the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation. In this case, x = $18,000, μ = $16,000, and σ = $5,000.

Substituting these values into the formula, we get z = (18,000 - 16,000) / 5,000 = 0.4.

Next, we can use a z-table or calculator to find the corresponding probability.

Looking up the z-score of 0.4 in the z-table, we find that the probability is approximately 0.6554, or about 65.54%.

Therefore, the probability that a randomly selected recent graduate has savings of $18,000 or more is approximately 65.54%.

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Answer:

Domain is all real numbers. Range is [36- negative infinity]

okay sorry

Step-by-step explanation:

i just wanted point

The central limit theorem,option (A) is correct

According to the central limit theorem, the following statement is correct:

a. Regardless of the underlying distribution, the distribution of the sum (or average) of a large number of independent variables with identical distributions will be approximately normal.

Regardless of the original distribution's shape, the central limit theorem states that independent and identically distributed variables tend to approximate a normal distribution when added together or averaged. We are able to draw conclusions about the parameters of the population based on the statistics of the sample because this is one of the fundamental principles of statistical inference.

The central limit theorem is unrelated to the other statements (b, c, and d). Statements b, c, and d all refer to common-cause variation rather than the central limit theorem, while statement d does not accurately describe the central limit theorem.

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Answer:

9

Step-by-step explanation:

There are 9 x's above 1 letter mailed.

Answer:

Given that average mass of an ant grams.

Given that average mass of a giraffe  Kilograms.

Now we have to find about how many times more mass does a giraffe have than an ant. Before carring out any comparision, we must make both units equal.

Like convert kilogram into gram or gram into kilogram.

I'm going to convert kilogram into gram using formula

1 Kg = 1000 g

So the average mass of a giraffe  grams.

Now we just need to divide mass of giraffe by mass of ant to find the answer.

=666666666.667

Hence final answer is  which is approx 666666666.667.

Hope this Helps!

Using the Ratio Test the series ∑(n³ / [tex]4^n[/tex]) converges. Option A is the correct answer.

To determine the convergence or divergence of the series ∑(n³ / [tex]4^n[/tex]), we can apply the Ratio Test.

The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms in a series is less than 1, then the series converges. If the limit is greater than 1 or it does not exist, the series diverges.

Let's apply the Ratio Test to the given series:

lim n → ∞ |([tex]a_n[/tex] + 1) / [tex]a_n[/tex]| = lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) / (n³ / [tex]4^n[/tex])|

We simplify the expression by multiplying by the reciprocal:

lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) × ([tex]4^n[/tex] / n³)|

Next, we simplify the expression inside the absolute value:

lim n → ∞ |((n + 1)³ × [tex]4^n[/tex]) / ([tex]4^{(n + 1)[/tex] × n³)|

Now, we can cancel out the common factors:

lim n → ∞ |(n + 1)³ / (4 × n³)|

Simplifying further:

lim n → ∞ |(n + 1) / (4n)|³

Taking the limit as n approaches infinity:

lim n → ∞ |(1 + 1/n) / 4|³

Since the limit of the absolute value of the ratio is less than 1 (as n approaches infinity), the series converges.

Therefore, the answer is:

A. Converges

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The question is -

Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.

∑ n = 1 to ∞ (n³ / 4^n)

lim n → ∞ |(a_n + 1) / a_n| = _______

A. Converges

B. Diverges

Answer:

utility cost, direct labor costs, cost of raw materials used in production

Answer:

I dot know good luck

Step-by-step explanation:

Answer:

the answer is 9

Step-by-step explanation:

The magnitude of the average induced electric field, e, in a loop can be expressed in terms of δφ, r, and δt.

When a magnetic field changes within a loop, it induces an electric field according to Faraday's law of electromagnetic induction. The magnitude of the average induced electric field, e, can be determined by the change in magnetic flux δφ, the radius of the loop r, and the change in time δt. The magnetic flux is a measure of the total magnetic field passing through the loop and is given by the product of the magnetic field strength and the area of the loop. As the magnetic field changes, the magnetic flux through the loop changes, leading to an induced electric field. The magnitude of this induced electric field is directly proportional to the rate of change of the magnetic flux, which is δφ/δt. Additionally, the magnitude of the induced electric field is inversely proportional to the radius of the loop, meaning a smaller radius will result in a stronger induced electric field. Therefore, the magnitude of the average induced electric field, e, can be expressed as e = (δφ/δt) / r.

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Answer:

[tex]15c - 1[/tex]

Step-by-step explanation:

[tex]3(5c + 3) - 10[/tex]

Apply the distributive property.

[tex]3(5c) + 3 \times 3 - 10[/tex]

Multiply 5 by 3.

[tex]15c + 3 \times 3 - 10[/tex]

Multiply 3 by 3.

[tex]15c + 9 - 10[/tex]

Subtract 10 from 9.

[tex]15c - 1[/tex]

The parametric equations for the circle with radius 4 and centered at (-3,4), traced clockwise starting at (-3,0), are x = -3 + 4cos(t) and y = 4 + 4sin(t), where t is the parameter representing the angle of rotation. The domain for these equations is 0 ≤ t ≤ 2π.

To obtain the parametric equations for the circle, we start by considering the general equation of a circle centered at (h,k) with radius r:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

In this case, the circle is centered at (-3,4) and has a radius of 4, so the equation becomes:

[tex](x + 3)^2 + (y - 4)^2 = 16[/tex]

To represent the circle parametrically, we can use the trigonometric functions cosine and sine to describe the x and y coordinates, respectively. We can rewrite the equation as:

(x + 3) = 4cos(t)

(y - 4) = 4sin(t)

Simplifying, we obtain:

x = -3 + 4cos(t)

y = 4 + 4sin(t)

These equations describe the x and y coordinates of points on the circle as a function of the angle t. The parameter t represents the angle of rotation around the circle. To trace the circle clockwise, we need to assign decreasing values to t. The domain for t is 0 ≤ t ≤ 2π, which corresponds to a full revolution around the circle.

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