Evaluate the expression: 2b + 9 when b = 3 *
A 3
B 11
C 14
D 15

The measure of angle ∠4 and angle ∠8 will be equal because they are corresponding angles. Then the correct option is D.

If two lines are parallel and the third line is transverse to it. Then the corresponding angles are equal to each other.

According to the equivalent angles postulate, if two parallel lines are intersected by a transverse, the corresponding inclination is identical.

From the diagram, the corresponding angles are given as,

∠1 = ∠5

∠2 = ∠6

∠3 = ∠7

∠4 = ∠8

The measure of angle ∠4 and angle ∠8 will be equal because they are corresponding angles. Then the correct option is D.

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The complete question is given below.

Which must be true by the corresponding angles

theorem?

a. ∠2 = ∠5

b. ∠1 = ∠6

c. ∠4 = ∠7

d. ∠4 = ∠8

The speed of the freight train is 30 mph, and the speed of the passenger train is 30 + 8 = 38 mph.

We have,

Let's denote the speed of the freight train as x mph.

Since the speed of the passenger train is 8 mph faster, we can denote the speed of the passenger train as (x + 8) mph.

To find the speeds of each train, we can use the formula:

Speed = Distance / Time

For the passenger train: (x + 8) = 280 / t, where t is the time taken to travel 280 miles.

For the freight train: x = 240 / t, where t is the time taken to travel 240 miles.

Since the times taken for both trains are the same, we can set the two equations equal to each other:

(x + 8) = 280 / t = x = 240 / t

Cross-multiplying the equation, we have:

(x + 8) t = x (280 / t)

xt + 8t = 280

xt - x = 240

Simplifying the equation, we get:

xt - x = 240

x(t - 1) = 240

Dividing both sides by (t - 1):

x = 240 / (t - 1)

Substituting the value of x in the first equation:

(x + 8) = 280 / t

240 / (t - 1) + 8 = 280 / t

Simplifying the equation, we get:

240t + 8(t - 1) = 280(t - 1)

240t + 8t - 8 = 280t - 280

248t - 8 = 280t - 280

280 - 8 = 280t - 248t

272 = 32t

t = 272 / 32 = 8.5

Substituting the value of t in the equation for x:

x = 240 / (t - 1) = 240 / (8.5 - 1) = 30

Therefore,

The speed of the freight train is 30 mph, and the speed of the passenger train is 30 + 8 = 38 mph.

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Answer:

the answer is 1 because 6 times 1 equals 6

Answer:

X=1

Step-by-step explanation:

Divide both sides by the same factor

6x=6

6x/6 =6/6

answer is X=1

Answer:

52.4 min

Step-by-step explanation:

100% of the times are between 49.2 min and 55.5 min.

48.8% of the times are between x and 55.5 min.

Write a proportion:

(55.5 − 49.2) / 1 = (55.5 − x) / 0.488

0.488 (55.5 − 49.2) = 55.5 − x

3.0744 = 55.5 − x

x = 52.4256

Rounded to the tenths place, the time is 52.4 min.

Both sides of the rectangle will be used to create a scale drawing of the field with some scale factor.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

Given lacrosse fields have

Length = 110 yd

Width = 60 yd

Scale drawing is generally similar but small in size drawing such that a constant scale factor is maintained.

Let's suppose the scale factor is 1/100

Means length in drawing → 110 × (1/100)

⇒ 1.1 yd

Width in drawing → 60 × (1/100)

Hence "Both sides of the rectangle will be used to create a scale drawing of the field with some scale factor".

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Answer:

  about 1.1%

Step-by-step explanation:

Given a moon has a diameter of 22% of the diameter its planet, you want the volume of the moon as a percent of the planet's volume.

The ratio of moon diameter to planet diameter is given as 22%. The ratio of moon volume to planet volume will be the cube of this scale factor:

  moon volume / planet volume = (0.22)³ ≈ 0.0106 = 1.06%

The volume of the moon is about 1.1% of the volume of the planet.

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Answer:

35

Step-by-step explanation:

Let me know if I'm wrong and you're welcome

Answer:

16 minutes on the elliptical trainer and 32 minutes on the treadmill.  

Step-by-step explanation:

We have the following relation for the training in both machines:

\( 400 cal = 9 cal/min*t_{1} + 8 cal/min*t_{2} \)    (1)

Where:

t₁: is the time spent on the elliptical trainer

t₂: is the time spent on the treadmill    

With:

\( t_{1} + t_{2} = 48 min \)    (2)  

From equation (2) we have:

\( t_{1} = 48 min - t_{2} \)    (3)

By entering equation (3) into (1):

\( 400 cal = 9 cal/min*(48 min - t_{2}) + 8 cal/min*t_{2} \)  

\( 400 cal = 432 cal - 9 cal/min*t_{2} + 8 cal/min*t_{2} \)

\( t_{2} = \frac{32 cal}{1 cal/min} = 32 min \)

Now, we can find t₁:

\( t_{1} = 48 min - t_{2} = 48 min - 32 min = 16 min \)              

Therefore, you should spend 16 minutes on the elliptical trainer and 32 minutes on the treadmill.

I hope it helps you!

Answer:

Volume = 7.912

Step-by-step explanation:

V = πr²h

V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )

V = 3.14 × 9/16 ×18/4

V = 3.14 × 0.56 × 4.5

V = 7.912

Answer:

A= 360

Step-by-step explanation:

360

       A linear equation has the conventional form Ax+By=C. A slope-intercept form equation (y=mx+b) must have the x and y on the same side of the equal sign and the constant on the opposite side in order to be converted to standard form. To relocate terms, use inverse operations.

 Linear equations come in three main types:

shape of a point-slope: y - y1 = m (x-x1)

typical form: Ax + By = c

Y = mx + b is the slope-intercept formula.

A linear equation with one variable is written in standard form as ax + b = 0, where a 0 and x is the variable. A linear equation with two variables is written as ax + by + c = 0, where the variables are a 0, b 0, x, and y.

A formula's initial sign is usually an equal sign (=).

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Answer:

20

Step-by-step explanation:

good luck!!

Answer:

24 or 20

Step-by-step explanation:

Answer:

I think A because we can't see the thing

Answer:

x=1

Step-by-step explanation:

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

As per the given details, the value of ff.ds over the region V bounded by the planes x = 0, y = 0, z = 0, z = 4, and the surface of the cylinder x² + y² = 9 in the first octant, where F = xî + xyj + 2k, is 81π.

The divergence theorem relates a flux fundamental across a closed floor S to a triple crucial over strong E enclosed by way of the surface.

It states that for a vector field F and a closed floor S that encloses a solid area E, the outward flux of F across S is equal to the triple necessary of the divergence of F over E.

Mathematically, the divergence theorem can be written as:

∫∫ F · dS = ∭ div(F) dV

To examine ff.Ds over the vicinity V bounded by using the planes x = zero, y = zero, z = zero, z = 4, and the floor of the cylinder x² + y² = 9 within the first octant, in which F = xî + xyj + 2k, we can use the divergence theorem. The first step is to locate the divergence of F:

div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 1 + x

Next, we want to discover the volume enclosed via the surface. The cylinder x² + y² = 9 inside the first octant is a round cylinder with radius 3 and top 4. Therefore, the volume enclosed with the aid of the floor is:

V = ∫∫R (4 - z) dA

= ∫0^3 ∫0^(2π) (4 - z) r dr dθ

= 18π

So,

∫∫S F · dS = ∭V div(F) dV

= ∭V (1 + x) dV

= ∫0^4 ∫0^3 ∫0^(2π) (1 + x) r dθ dz dr

= 81π

Therefore, the value of ff.Ds over the place V bounded through the planes x = 0, y = 0, z = zero, z = four, and the surface of the cylinder x² + y² = 9 inside the first octant, where F = xî + xyj + 2k, is 81π.

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Answer:

C: A= 47 1/2

Step-by-step explanation:

You multiply the height by the base (which is on top), to get 47 and 1/2

Answer: your answer would be 5/16th :)

Answer:

5/16

Step-by-step explanation:

The common ratio is -5/2 / 5 = -1/2

Xn = 5 × (-1/2)^(n-1)

X5 = 5 × (-1/2)^(5-1)

X5 = 5 × (-1/2)^(4) = 5/16

So, in this case, the length of each of the equal sides is: 17 / \(\sqrt{2}\) ≈ 12.02

An isosceles triangle is a triangle in which two sides have the same length. This means that two of the three angles in the triangle are also equal in measure. The side that is not congruent to the other two sides is called the base of the triangle, and the angles opposite the congruent sides are called the base angles. In an isosceles triangle, the base angles are always equal in measure.

Isosceles triangles are a common shape in geometry and can be found in many real-world applications. They have special properties that make them useful in various fields of mathematics, such as trigonometry and geometry. For example, the base angles of an isosceles triangle are always equal, so if you know the measure of one of the base angles, you can determine the measure of the other base angle using the fact that the sum of the angles in a triangle is 180 degrees.

given by the question.

In an isosceles triangle with two equal angles of 45 degrees and a third angle of 90 degrees, the two equal sides are opposite the 45 degree angles, and the third side is opposite the 90 degree angle. Let's call the length of the missing side "x".

Using the Pythagorean theorem, we know that in a right triangle with legs of equal length (which is the case for the two 45-degree angles), the length of the hypotenuse is. \(\sqrt{2}\) times the length of the legs.

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At a 5% level of significance, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the percentage of vegetarians in age group 18 to 35 years is higher than 5%.

To test the hypothesis that the percentage of vegetarians is higher in the age group 18 to 35 years at a 5% level of significance, we can use a hypothesis test with the following null and alternative hypotheses:

Null hypothesis (H0): The percentage of vegetarians in the age group 18 to 35 years is equal to 5%.

Alternative hypothesis (Ha): The percentage of vegetarians in the age group 18 to 35 years is greater than 5%.

We can conduct a one-tailed z-test to test this hypothesis, using the following formula:

z = (p - P0) / sqrt(P0 * (1 - P0) / n)

where:

p is the sample proportion of vegetarians in the age group 18 to 35 years

P0 is the hypothesized proportion (5%)

n is the sample size

We will reject the null hypothesis if the calculated z-value is greater than the critical z-value corresponding to a 5% level of significance (one-tailed test).

Assuming a sample of size n = 100, if we find that 10 people in the sample identify themselves as vegetarians, then the sample proportion is:

p = 10/100 = 0.1

Using the formula above, we can calculate the z-value:

z = (0.1 - 0.05) / sqrt(0.05 * 0.95 / 100) = 1.96

The critical z-value for a one-tailed test at a 5% level of significance is 1.645 .

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The value of angle x is 133 degree

And the equation of line be of the form,

⇒  y - y₁ = 133(x - x₁)

In the given line,

one angle is of 47 degree

And other is x degree

To find the value of x,

Since we know that,

The angle  of line is 180 degree.

Therefore,

⇒ x + 47 = 180

⇒         x = 133 degree

Therefore slope of this line be 133 degree

Now let this line is  passing through (x₁, y₁)

Hence,

The equation of  line be,

⇒ y - y₁ = (slope)(x - x₁)

⇒  y - y₁ = 133(x - x₁)

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

Answer:

a: t= arccos (h/7)

b: 1 cm = 1.427 s, 3 cm = 1.128 s, 5 cm = .775 s

Step-by-step explanation:

a: I'm assuming the equation is h=7cos(t)

h/7=cos(t)

t= arccos (h/7)

b: plug this equation in demos and then put x=1, x=2, x=3 and see where the lines intersect the graph of y=arccos (x/7), the y value will be the answer.

Therefore, a sample size of at least 962 students should be taken to get a distribution of means of the samples with a standard deviation of 10.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much, on average, the individual data points deviate from the mean of the dataset. A smaller standard deviation indicates that the data points tend to be closer to the mean, while a larger standard deviation indicates that the data points are more spread out. The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean.

Here,

To calculate the sample size required to get a distribution of means with a standard deviation of 10, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score (corresponding to the desired level of confidence)

σ = population standard deviation

E = desired margin of error (which is the standard deviation of the distribution of sample means)

In this case, we want a distribution of means with a standard deviation of 10, so E = 10.

To determine the z-score, we need to choose a level of confidence. Let's say we want a 95% level of confidence, which corresponds to a z-score of 1.96.

Plugging in the numbers we have:

n = (1.96 * 70 / 10)²

n = 961.54

We can't have a fractional sample size, so we need to round up to the nearest whole number:

n = 962

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Answer:

A. Reflection

Step-by-step explanation:

I believe the answer would be reflection

Answer:

\(\displaystyle 380,13271108...\:yd.^2\)

Step-by-step explanation:

\(\displaystyle {\pi}r^2 = A \\ \\ 11^2\pi = A \hookrightarrow 121\pi = A \\ \\ \boxed{380,13271108... = A}\)

If you want to follow what the exercise wants, then multiplying \(\displaystyle 3,14\)by the square of the radius will give you \(\displaystyle 379,94\:yd.^2.\)

I am joyous to assist you at any time.

Answer:

y-axis

negative

positive

Step-by-step explanation:

in that order.

Recall that

cos²(x) + sin²(x) = 1

for any x. Also, remember that cotangent is defined as

cot(x) = cos(x) / sin(x)

We're given that cos(t ) = 5/13 and cot(t ) < 0, which means sin(t ) must be negative. So when we solve for sin(t ) in the first relation, we have to take the negative square root:

sin²(t ) = 1 - cos²(t )

sin(t ) = -√(1 - cos²(t ))

sin(t ) = -√(1 - (5/13)²) = -12/13

Then

cot(t ) = (5/13) / (-12/13) = -5/12

Answer:

isnt it 72

Step-by-step explanation:

since it is that kind of triangle