(2x + 3)(3x + 1) = 11x + 30

Solve for x

Answer: The other angle would be 60 degrees.

Step-by-step explanation:

Answer:

Step-by-step explanation:

12

Answer: 3:1

Step-by-step explanation:

From the question, we are informed that a gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket.

We are further told that the bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket.

Based on the explanation given in the question, the gear ratio for the bike would be the ratio of 36 to 12. This will be:

= 36:12

Since 12 is a common factor. It can be further reduced to 3:1.

Therefore, the gear ratio is 3:1

Answer:

\(\frac{3}{1}\)

Step-by-step explanation:

That's the answer

Answer:

Option C.

Step-by-step explanation:

The given absolute value inequality is

\(|x+12|+5<27\)

Isolate the absolute value by subtracting 5 from both sides.

\(|x+12|+5-5<27-5\)

\(|x+12|+0<22\)

\(|x+12|<22\)

Therefore, the correct option is C.

We can further solve this, to find the solution of the given inequality.

\(-22<x+12<22\)

Subtract 12 from each sides.

\(-22-12<x+12-12<22-12\)

\(-34<x<10\)

The solution of given inequality is \(-34<x<10\).

Therefore, the linearization of f(x) = cos(x) at a = π/2 is L(x) = π/2 - x.

The linearization of a function f(x) at a point a is given by:

L(x) = f(a) + f'(a)(x - a)

where f'(a) denotes the derivative of f(x) evaluated at x = a.

In this case, we have:

f(x) = cos(x)

a = π/2

First, let's find f'(x):

f'(x) = -sin(x)

Then, we can evaluate f'(a):

f'(π/2) = -sin(π/2) = -1

Next, we can plug in the given values into the formula for linearization:

L(x) = f(a) + f'(a)(x - a)

L(x) = cos(π/2) + (-1)(x - π/2)

L(x) = 0 - x + π/2

L(x) = π/2 - x

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Answer:

x = 6

Step-by-step explanation:

The given statement is "Eighteen is six less than four times a number".

Let the number be x.

ATQ,

18 = 4x-6

Taking like terms together,

18+6 = 4x

24 = 4x

x = 6

Hence, the value of x is 6.

Answer:

Step-by-step explanation:

it is A cuz if you do it the other way it would be wrong which is D

ΔWCO and ΔPIG are congruent by SSS.

Option B is the correct answer.

There are ways to prove that two triangles are congruent.

- Side-Side-Side (SSS) Congruence.

The three sides of one triangle are equal to the corresponding three sides of another triangle.

- Side-Angle-Side (SAS) Congruence.

The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.

- Angle-Side-Angle (ASA) Congruence.

The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

- Angle-Angle-Side (AAS) Congruence.

We have,

From ΔWCO and ΔPIG

The ratio between the corresponding sides is same.

i.e

WC/GP = WO/GI = 7/21 = 5/15 = 1/3

Now,

Since the ratio of the two corresponding sides in the two triangles are same,

The ratio of the remaining corresponding sides will also be the same.

Now,

C0 = IP = 1/3

So,

ΔWCO and ΔPIG are congruent by SSS.

Thus,

ΔWCO and ΔPIG are congruent by SSS.

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The x-intercepts (zeros) of the function are x = -5 and x = -6.

The factored form of the quadratic function is y = (x + 5)(x + 6). To find the x-intercepts (zeros) of the function, we set y to zero and solve for x. Setting y = 0 gives:

0 = (x + 5)(x + 6)

Using the zero-product property, we know that the product of two factors is zero if and only if at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for x:

x + 5 = 0 --> x = -5

x + 6 = 0 --> x = -6

To plot their points, you would mark the coordinates (-5, 0) and (-6, 0) on the coordinate plane. These points represent the x-intercepts of the function, where the parabola intersects the x-axis.

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The volume of the given solid is 2592π.

We need to find the volume of the solid enclosed by the paraboloids

y = x^2 + z^2 and y = 72 − x^2 − z^2.

By symmetry, the solid is symmetric about the y-axis, so we can use cylindrical coordinates to set up the triple integral.

The limits of integration for r are 0 to √(72-y), the limits for θ are 0 to 2π, and the limits for y are 0 to 36.

Thus, the triple integral for the volume of the solid is:

V = ∫∫∫ dV

= ∫∫∫ r dr dθ dy (the integrand is 1 since we are just finding the volume)

= ∫₀³⁶ dy ∫₀²π dθ ∫₀^(√(72-y)) r dr

Evaluating this integral, we get:

V = ∫₀³⁶ dy ∫₀²π dθ ∫₀^(√(72-y)) r dr

= ∫₀³⁶ dy ∫₀²π dθ [(1/2)r^2]₀^(√(72-y))

= ∫₀³⁶ dy ∫₀²π dθ [(1/2)(72-y)]

= ∫₀³⁶ dy [π(72-y)]

= π[72y - (1/2)y^2] from 0 to 36

= π[2592]

Therefore, the volume of the given solid is 2592π.

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Answer:hundredths

Step-by-step explanation:

Just know

Answer:

I think it’s 10

Step-by-step explanation:

The height of the cone is increasing at a rate of 16/9 units per second when the volume is 12 pi cubic units and the radius is 3 units.

To find the rate at which the radius is changing when the volume of the cone is 12 pi cubic units and the radius is 3 units, we can use related rates.

Given:
- Volume rate of change: dv/dt = 28 pi cubic units per second
- Radius: r = 3 units
- Volume: V = 12 pi cubic units
- Radius rate of change: dr/dt = 1/2 unit per second

We can use the formula for the volume of a cone: V = (1/3) pi r^2 h, where h is the height of the cone.

Since we only have the radius, we need to find the height in order to calculate the rate of change of the radius.

Given that the radius is 3 units, we can use the formula for the volume to solve for the height:
12 pi = (1/3) pi (3^2) h

Simplifying the equation, we get:
12 = (1/3) * 9 * h
h = 12 / (1/3 * 9)
h = 4

Now, we can differentiate the volume equation implicitly with respect to time (t) to find the relationship between the volume and radius rates of change:

dV/dt = (1/3) pi * (2r * dr/dt) * h + (1/3) pi * r^2 * dh/dt

Plugging in the given values:
28 pi = (1/3) pi * (2 * 3 * (1/2)) * 4 + (1/3) pi * (3^2) * dh/dt

Simplifying the equation, we get:
28 = 12 + 9 * dh/dt
dh/dt = (28 - 12) / 9
dh/dt = 16/9

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Given:

The total 5 yards of thread on the spool.

Convert yard into meters.

For 5 yards to meters is,

Allison uses 3.5 meters of the thread, the thread remains is,

Answer: The thread left will be approximately 1.072 meters.

Answer:

x= -16

Step-by-step explanation:

-2x+5=37

-2x=37-5

-2x=32

x= -16

Answer:

x= -16

Step-by-step explanation:

The goal in this problem is to get X on one side by itself.

We know that the opposite of subtraction is addition and the opposite of multiplication is division.

so to get 5 over to the right side, we need to subtract.

-2x+5=37 >>-2x= 37-5= 32

your problem now reads -2x= 32

We still have -2 on the left side and we need it to go to the right side so that X is by  itself. The opposite of multiplication is division, so we will need to divide

-2x=32÷-2 >> x=-16

System of inequalities that represents this scenario is 7x + 11y ≥ 700 (the total amount of merchandise sold must be at least $700) y ≥ 50 (at least 50 coffee mugs must be sold)

Dominique is selling merchandise for a school fundraiser. To meet her goals, she must sell at least $700 worth of merchandise, including at least 50 coffee mugs.

Let x be the number of calendars sold and y be the number of coffee mugs sold. The revenue from selling x calendars and y coffee mugs can be calculated as follows:

Revenue = (Price per calendar) x (Number of calendars sold) + (Price per coffee mug) x (Number of coffee mugs sold)

Given that calendars are being sold for $7 each and coffee mugs are being sold for $11 each, the revenue equation can be expressed as:

Revenue = 7x + 11y

To meet the fundraising goal of selling at least $700 worth of merchandise, the total revenue generated from the sale of calendars and coffee mugs must be at least $700. Hence, we can express this as the inequality:

7x + 11y ≥ 700

In addition, Dominique must sell at least 50 coffee mugs. This can be expressed as the inequality:

y ≥ 50

Combining both inequalities, we get the system of inequalities:

7x + 11y ≥ 700 and y ≥ 50

This system of inequalities represents the scenario where Dominique must sell at least $700 worth of merchandise, including at least 50 coffee mugs. The first inequality ensures that the total revenue generated from the sale of calendars and coffee mugs meets the fundraising goal, while the second inequality ensures that at least 50 coffee mugs are sold.

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Answer:

\(1\frac{1}{3}\)  

Step-by-step explanation:

Write a proportion comparing the Oliva Oil to Vinegar = Oliva Oil to Vinegar.

\(\frac{3/4}{1/2} = \frac{2}{?}\)

3/4 ? = 2(1/2)

3/4? = 1

  ? = 1 ÷ 3/4

  ? = 1 × 4/3

  ?  = 4/3

  \(? = 1\frac{1}{3}\)

Answer: a

Step-by-step explanation:  a b

The length of the straw is 3.74 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangular box,

Length (l) = 2 inches

Width (w) = 1 inches

Height (h) = 3 inches

Here, The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

⇒ s = √ l² + w² + h²

⇒ s = √ 2² + 1² + 3²

⇒ s = √ 4 + 1 + 9

⇒ s = √ 14

⇒ s = 3.74 inches

Thus, The length of straw = 3.74 inches

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The length of the straw will be 3.7416  inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²

Here,

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 2 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X²=14

X=√14

i.e. X=3.7416

We get, X= 3.7416 (in radical form)

Hence, the length of the straw will be  5.91607 inches.

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Answer: Third option

Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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A 90% confidence interval for the proportion of adults who are worried about having enough money for retirement is (0.5031, 0.5396).

To construct a 90% confidence interval for the proportion of adults who are worried about having enough money for retirement, follow these steps:

1. Determine the sample proportion (p- hat):
p- hat = number of adults worried / total number surveyed
p- hat = 569 / 1094
p- hat ≈ 0.5199

2. Determine the confidence level (90%) and find the corresponding z-score using a z-table or calculator. For a 90% confidence interval, the z-score is approximately 1.645.

3. Calculate the standard error (SE):
SE = sqrt((p- hat * (1 - p- hat)) / n)
SE = sqrt((0.5199 * (1 - 0.5199)) / 1094)
SE ≈ 0.0156

4. Construct the confidence interval using the sample proportion, z-score, and standard error:
Lower limit: p- hat - (z-score * SE)
Lower limit: 0.5199 - (1.645 * 0.0156)
Lower limit ≈ 0.4938

Upper limit: p- hat + (z-score * SE)
Upper limit: 0.5199 + (1.645 * 0.0156)
Upper limit ≈ 0.5460

A 90% confidence interval for the proportion of adults who are worried about having enough money for retirement is (0.4938, 0.5460).

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Answer:

f(x)=|x-6|

Step-by-step explanation:

Translation is a shift. Opposite how many units it moved. In with the x because that's side to side. If it was not with the x, it's up and down.

The transformation of a function may involve any change. The equation of g(x) is |x-6|.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift:

Stretching:

Given that the function f(x)=|x|, this function is needed to be translated 6 units to the right. Therefore, the new function can be written as,

g(x) = f(x-6)

      = |x - 6|

Hence, the equation of g(x) is |x-6|.

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Part 1:

(a) Fill in the missing table cells:

Table 1: Impact Strength (ft-lb/in)

1 1 2 3 4 5 5

Point Values

55 56 55 50 46

(b) The Sum of Squares equals: 73.2

(c) This variance equals: 18.3

(d) The standard deviation equals: 4.278

(e) The deviation for the first observation equals: 2.6

(f) The Z-score for the fifth observation equals: -1.4961

Part 2:

We wish to convert from foot-pound/in to J/m, so let y be the strength in J/m. There is 1 ft-lb/in for every 53.35 J/m.

G) -

H) s2y =

I) Sy =

J) The Z-score for the fifth transformed observation is:

Part 1:

(a) The missing table cells are not provided in the question.

(b) The Sum of Squares is calculated by summing the squares of the deviations of each data point from the mean. Since the values are not provided, we cannot calculate the Sum of Squares.

(c) Variance is the average of the squared deviations from the mean. It is calculated by dividing the Sum of Squares by the number of data points. In this case, the variance is given as 18.3.

(d) Standard deviation is the square root of the variance. It is calculated as the square root of the variance. In this case, the standard deviation is given as 4.278.

(e) The deviation for the first observation is provided as 2.6. It represents the difference between the first observation and the mean.

(f) The Z-score for an observation is a measure of how many standard deviations it is away from the mean. The Z-score for the fifth observation is given as -1.4961.

Part 2:

In order to convert from foot-pound/in to J/m, we need to use the conversion factor of 1 ft-lb/in = 53.35 J/m.

G) - The missing value is not provided in the question.

H) The variance of the transformed variable, y, can be calculated by multiplying the variance of the original variable, x, by the square of the conversion factor (a^2). However, since the variance of x is not provided, we cannot calculate s2y.

I) The standard deviation of the transformed variable, y, can be calculated by multiplying the standard deviation of the original variable, x, by the absolute value of the conversion factor (|a|). However, since the standard deviation of x is not provided, we cannot calculate Sy.

J) The Z-score for the fifth transformed observation can be calculated by subtracting the mean of the transformed variable from the fifth transformed observation and then dividing it by the standard deviation of the transformed variable.

However, since the mean and standard deviation of the transformed variable are not provided, we cannot calculate the Z-score.

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The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

According to the question,

91 pts nine percent of Americans have rh-negative o blood type.

In a random sample of 200 Americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% = ?

by Using central limit theorem,

P(p cap < p) = P(Z<p cap-p/√p(1-p)/n)

so,

P(p cap < 0.12) = P(Z<0.12-0.09/√(0.09×0.91/200)

= P(Z<1.4825)

= 0.9309 (from Z table)

= 0.93 (Rounded to second decimal place)

so, The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

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Answer: \(y-1=\dfrac32(x+3)\)

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = \(\dfrac{d-b}{c-a}\)

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =\(\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}\)

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

\((y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)\)

Required equation: \(y-1=\dfrac32(x+3)\)

Answer:

15

Step-by-step explanation:

According to propagation rule,

\(\frac{9}{3} =\frac{x}{5} \\45=3x\\x=15\)

Therefore, option (B) is correct

Answer: x=-15

Step-by-step explanation:

-1 = 4 + x/3

-1-4=4-4+x/3

-5=x/3

-5*3=x*3/3

-15=x*1

x=-15

\(-1=4+\frac{x}{3}\\ \\-1(-4)=4+\frac{x}{3}-4\ \ \ \ \ \ \ \ \ \ justify:subtract\ by\ 4\ on\ both\ sides\\\\(3)-5=x/3(3)\ \ \ \ \ \ \ \ \ justify:\ multiply\ by\ 3\ on both sides\\\boxed{x=-15}\)