In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle OPQ = (9x-19)^{\circ}m∠OPQ=(9x−19) ∘ , \text{m}\angle PNO = (2x+5)^{\circ}m∠PNO=(2x+5) ∘ , and \text{m}\angle NOP = (3x+16)^{\circ}m∠NOP=(3x+16) ∘. Find \text{m}\angle NOP. M∠NOP

The exponential equation after solving gives -26.

Exponential equations are equations where the independent variable, x is in the exponent.

The given equation is,

[tex]5^{7x+5}[/tex] = [tex]125^{2x-7}[/tex]

We know that 125 = 5³

[tex]5^{7x+5}[/tex] = [tex]5^{3(2x-7)}[/tex]

The base in the both sides of the equation is 5.

So,

7x + 5 = 3(2x - 7)

7x + 5 = 6x - 21

7x - 6x = -21 - 5

x = -26

Hence the value of x is -26.

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If the slope of a staircase is 0. 95 and rises with 210, then the run is:

221.05 units.

In this problem, we can use the formula for the slope of a staircase, which is given by:

where "rise" is the vertical height of the staircase and "run" is the horizontal distance of the staircase.

We are given the slope of the staircase as 0.95 and the rise as 210. We can substitute these values in the formula and solve for the run:

Multiplying both sides by run, we get:

Dividing both sides by 0.95, we get:

Simplifying the expression, we get:

Therefore, the run of the staircase is approximately 221.05 units.

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The inequality showing the maximum number of days he can rent a car is 10d ≤ 75.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that Passion has a budget of $75 and wants to rent a car for a trip. A fixed daily fee of 10 is charged.

The product of the number of days and the rent per day should be less than the amount he has.

The inequality mathematically can be written as:-

10t ≤ $75

Therefore, the inequality 10d ≤75 shows how many days he can rent an automobile for the most.

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The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'y' is given by the tangent of the angle 27°. Then we have

tan 27° = y / 350

y = 350 tan 27°

y = 178.3

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

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The missing diagram is given below.

Answer: 78.39 thousand, (78,390)

Step-by-step explanation:

Using the quadratic formula with this gives us two answers, 78.39 and -65.39. Since a negative answer doesnt make sense in this context, we will go with 78.39 thousand pens, (78,390 pens). The limit on x however doesn't seem to make sense as it says x </= 25 and x>/= 0. The only two answers are both above and below this limit.

Answer:  -2 ±√6
                    2

Step-by-step explanation:
Use the quadratic formula - its better to separate it into two parts
Δ = b²-4ac
   = 4² -4(2*-1)
   = 16 + 8

∴ Δ = 24
Then
x = (-b ± √Δ) ÷ 2a
  = (-4 ± √24) ÷ 4
  = (-4 ± 2√6) ÷ 4 (simplify the surd form)
∴ x = -2 ±√6   (simplify by crossing out the 2's)
             2

The total volume of the space dome theatre is 41867 m³.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The space dome theatre has a base radius of 20m.

Therefore, The volume of the hemispherical dome is,

= (2/3)π(20)³.

= (2/3)π×8000.

= (16000/3)π m³.

And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.

Therefore, The volume of the cylindrical shape is,

= π(20)²×20.

= 8000π m³.

And, The total volume is the sum of the volumes of two shapes,

= 8000π + (16000/3)π m³.

= [(24000 + 16000)/3]π m³.

= (40000/3)π m³.

= 41867 m³.

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In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.

[tex]\text{Height } = h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]

The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone.

If we rearrange this formula to solve for h, we get h = 3V / (πr²). This means that the height of a cone is directly proportional to the volume and inversely proportional to the square of the radius.

a. If the radius of a cone is 2 inches and its volume is given, we can find its height by plugging in the values of V and r into the formula for h.

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]

b. Similarly, if the radius is 3 inches, the height would be:

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (3^2)} = \frac{3V}{9\pi}[/tex]

c. If the radius is 6 inches, the height would be:

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (6^2)} = \frac{3V}{36\pi}[/tex]

In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.

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Answer:

could write 21 + 38 + 75 = 134

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

100x2=200

200-100=100!

Answer:

100

Step-by-step explanation:

First do 100 multiplied by 2 you will then get 200

Next step is to do 200 subtracted by 100 which will give you 100.

There is no mode of the number of girl in the three classes.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode.

Given:

The data for boys: 15, 12, 12

The data for Girls: 14, 12, 16

As, mode is the most repeating data.

We can see that the data repeats in boys but not for the Girls.

So, number of boys have the mode but the number of girls do not have the mode.

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Answer:

Step-by-step explanation:

The standard form of the quadratic function that represents the area of the garden is: G(x) = - 2x² + 20x

Mrs Miller has 20 ft of fencing to put around three sides of the garden.

Let us assume that l represents the length of the garden.

Here x represents the width of the rectangular garden.

So, l = 20 - 2x

We know that the formula for the area of rectangle is:

A = length × width

Let G(x) be a function that represents the area of the garden.

Using above formula,

G(x) = x × l

G(x) = x(20 - 2x)

G(x) = 20x - 2x²

G(x) = - 2x² + 20x

Therefore, the required quadratic function is: G(x) = - 2x² + 20x

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Find dthe complete question below.

The solution to the inequality are the region in the shaded area and the graph is attached

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

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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The solution of x in the triangle is 11.5

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

The triangle

Using the Pythagoras theorem, we have the following equation

x^2 = 13^2 - 6^2

Evaluate the expression

x^2 = 133

Take the square roots of both sides

x = 11.5

Hence, the solution is 11.5

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Explanatory variable: Cooling time in seconds

Response variable: Impact strength in kj/m2

To find the equation of the linear model that describes the relationship between the predicted value of the response and the explanatory variable, we can use linear regression analysis. Using a statistical software or a calculator, we can find the slope and intercept of the line that best fits the data.

The equation of the linear model is:

Impact strength = -1.23 * Cooling time + 62.61

R-squared (R2) is a statistical measure that represents the proportion of the variance in the dependent variable (impact strength) that is explained by the independent variable (cooling time). It ranges from 0 to 1, with higher values indicating a better fit of the model.

Based on the value of R2, we can say how much of the variation in impact strength can be explained by cooling time. The closer R2 is to 1, the better the model fits the data, and the more likely it is that the impact strength is affected by cooling time. A value of 1 would indicate that all the variation in impact strength is explained by cooling time, while a value of 0 would indicate that cooling time has no effect on impact strength.

          Without knowing the actual value of R2, we cannot say for sure what the relationship is between the explanatory and response variables. However, if the value of R2 is high (close to 1), we can conclude that cooling time has a significant effect on impact strength. If the value of R2 is low (close to 0), we cannot conclude that cooling time has a significant effect on impact strength.

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Answer:

true

the t-value does change depending on the number of data points collected.

It is true that the t-value can change depending on the number of data points collected.

The t-value is a statistic used in hypothesis testing to determine whether a sample mean is significantly different from a population mean.

The formula for calculating the t-value includes the sample size (n) in the denominator, which means that as the sample size increases, the t-value decreases (assuming all other factors remain constant).

In other words, a larger sample size will generally result in a smaller t-value, which in turn may affect the interpretation of the results of a hypothesis test. Therefore, the t-value can change depending on the number of data points collected.

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Answer:

Each one-inch binder costs $2.67 and each two-inch binder costs $6.

Step-by-step explanation:

Let's call the cost of a one-inch binder "x" and the cost of a two-inch binder "y".

From Hansen's purchase, we know that 3x + 2y = $20.

From Pam's purchase, we know that 3x + 5y = $32.

We can use these two equations to solve for the cost of each size of binder. If we subtract the first equation from the second, we get:

2y = $32 - $20 = $12

So, y = $6, which is the cost of a two-inch binder.

Next, we can plug this value back into either of the original equations to find the cost of a one-inch binder:

3x + 2($6) = $20

Expanding the right side, we get:

3x + $12 = $20

Subtracting $12 from both sides, we get:

3x = $8

Finally, dividing both sides by 3, we find that:

x = $2.67

So, each one-inch binder costs $2.67 and each two-inch binder costs $6.

Answer:139.33 or 139 ft high

Step-by-step explanation: since building A is three times as high as building B, we can use the equation 418/3=B, which results in 139.33, and if rounding it needed you could round it to 139

Answer:

12.2 pints

Step-by-step explanation:

In all means add.  Add the two decimals together.

4.8 + 7.4

12.2 pints

The linear inequality that is graphed with y > –x – 2 to create the given solution set is D. y < x + 1

One of the line is having the y intercept -2 and slope -1 having the equation y=-x-2. The shaded region is having the inequality y>-x-2.

The other line is having the y intercept 1 and slope of 1. Hence equation of line is y=x+1.

The shaded part is above the line .The inequality region is represented by the inequality y <x+1.

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Which linear inequality is graphed with y > –x – 2 to create the given solution set?

A=y > x + 1

B=y < x – 1

C=y > x – 1

D=y < x + 1

The triangles are congruent by SSS and the transformation rule is (x, y) ⇒ (x - 4, y)

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

Triangles EFD and GH

The triangles are congruent because they have equal corresponding side lengths

The corresponding sides of the triangles are congruent

So, the congruent statement is SSS

From the figure, we can see that:

EFD is shifted left by 4 units

So, the rule is

(x, y) ⇒ (x - 4, y)

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Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

Word problems in Mathematics are mathematical approaches we make use of in our ongoing day to day activities. Algebra leading to word problems usually consist of numbers, variables, and its arithmetic operations.

Ahlam bought goods worth = $90, If she gave the shopkeeper $100, then she will collect $100 - $90 = $10 back.

But if the shopkeeper did not have an exact balance and Ahlam decided to give the shopkeeper $x to get a balance of $25.

Then we can write the expression as:

10 + x = 25

x = 25 - 10

x = 15

Therefore, we can conclude that Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

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Answer:

Solution and calculation given below.

The solution is, the distance of the towns is 11.88 km

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have,

So this can be solve by solving the distance of the plane and the town to the west and also the distance of the plane to the town to the east.  

So the town with an angle of depression of 34 degrees

Let x be the distance of the plane and town  

Cos 34 = x / 8

x = 8 cos 34

x = 6.63 km  

So the town with an angle of depression of 49 degrees

Let y be the distance of the plane and town  

Cos 49 = y / 8

y = 8 cos 49

y = 5.25 km  

so the distance of the towns is 5.25 + 6.63 = 11.88 km

Hence, The solution is, the distance of the towns is 11.88 km.

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complete question:

An airplane is flying between two towns at an altitude of 8km. One town is to the west of the plane and the other is to the east. The angle of depression to one town in de34grees and to the other town is 49degrees. What is the distance between the two towns

Answer: B

Step-by-step explanation:

if r is close to 1 (or -1) it means the relationship is strong, -0.2041 is really close to 0 so the data is most likely scattered and the association is weak

Answer:

Strong

Step-by-step explanation:

edge 2023

Answer:

Domain is x-value and range is y-values

Step-by-step explanation:

The inequality is c ≤ 187, where c is the number of 130-kg crates that can be added to the shipping container

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of 130-kg crates that can be added to the shipping container be c

The greatest weight the shipping container can hold = 27,500 kg

The weight that is already loaded = 3,100 kg

So , the total number of 130kg weights = 130c

Substituting the values in the equation , we get

27500 - 3100 ≥ 130c

130c ≤ 24,400

Divide by 130 on both sides of the equation , we get

c ≤ 187.69

So , the value of c is 187 crates

Hence , the inequality is c ≤ 187

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The parcel is 30 acres in size, calculated as 10 acres for the NW 1/4 of the SE 1/4 and 20 acres for the S 1/2 of the SW 1/4 of the NE 1/4.

To solve the problem, we need to know the size of the quarter sections that are being referred to. In the United States, a quarter section is 160 acres.

Using this information, we can break down the given parcel as follows:

NW 1/4 of the SE 1/4: This represents 1/16 of a section, or 10 acres (160 acres / 16 * 1 = 10).

S 1/2 of the SW 1/4 of the NE 1/4: This represents 1/8 of a section, or 20 acres (160 acres / 8 * 1/2 = 20).

To find the total size of the parcel, we simply add these two areas together:

(10 + 20 )acres = 30 acres

Therefore, the parcel is 30 acres in size.

In the United States, a section of land is a unit of area measurement used in land surveys, and it is equal to 640 acres. A quarter section is, therefore, one-fourth of a section, or 160 acres.

The given parcel is described as two parts. The first part is the northwest quarter of the southeast quarter, which is equivalent to one-sixteenth of a section or 10 acres (1/4 x 1/4 x 160 acres = 10 acres).

The second part is the south half of the southwest quarter of the northeast quarter, which is equivalent to one-eighth of a section or 20 acres (1/4 x 1/4 x 1/2 x 160 acres = 20 acres).

To find the total size of the parcel, we add the area of the two parts: 10 acres + 20 acres = 30 acres. Therefore, the parcel is 30 acres in size.

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