70 out of 550 questions on a standardized test are math questions. what percent of the test is mathematics?

Answer:

see explanation

Step-by-step explanation:

Since the marked angles are congruent, let them be x

(6)

The sum of the interior angles of a quadrilateral = 360°

Sum the angles and equate to 360

x + x + 120 + 90 = 360

2x + 210 = 360 ( subtract 210 from both sides )

2x = 150 ( divide both sides by 2 )

x = 75

Then ∠ X = ∠ Y = 75°

---------------------------------------------------------------------

(7)

The sum of the interior angles of a hexagon = 720°

Sum the angles and equate to 720

x + x + 108 + 103 + 149 + 90 = 720

2x + 450 = 720 ( subtract 450 from both sides )

2x = 270 ( divide both sides by 2 )

x = 135

Then ∠ X = ∠ Y = 135°

Answer:

Step-by-step explanation:

Sum of the interior angles of a regular polygon:

Quadrilateral has sum of angles:

Sum the given angles and consider x = y as marked congruent:

Hexagon has sum of angles:

Sum the given angles and consider x = y as marked congruent:

Answer:

221 m

Step-by-step explanation:

Let h = height of dam

tan 33 = h/340

340 tan 33 = h

h = 221 m

The height of the dam to the nearest meter will be 221 m.

The vertical distance between the object's top and bottom is defined as height. It is measured in centimeters, inches, meters, and other units.

From the trigonometry;

[tex]\rm tan \theta = \frac{P}{B} \\\\ \rm tan 33^0 = \frac{h}{340} \\\\ h=221 \ m[/tex]

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a) For these 24 dog sitters, as experience increases, the amount charged tends to increase.

b)  For these 24 dog sitters, there is a positive correlation between experience and amount charged.

c) Using the line of best fit, we would predict that a dog sitter with 5 years of experience would charge approximately $16.5 per hour.

(a) For these 24 dog sitters, as experience increases, the amount charged tends to increase. This means that the amount charged per hour increases with an increase in years of experience for dog sitters.

(b) For these 24 dog sitters, there is a positive correlation between experience and amount charged. The points on the scatter plot show a generally upward trend, and the line of best fit is also sloping upward.

(c) Using the line of best fit, we would predict that a dog sitter with 5 years of experience would charge approximately $16.5 per hour. This can be determined by locating the point on the X-axis corresponding to 5 years of experience, and then drawing a vertical line to the line of best fit. From there, we can draw a horizontal line to the Y-axis to find the predicted amount charged per hour, which is about $16.5.

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Answer:

56 degree and 68 degree

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Answer:

62°

Step-by-step explanation:

Since the triangle is isosceles then the 2 base angles are congruent.

Given there is one angle measuring 56° then it must be the vertex angle.

Thus the 2 congruent base angles are

[tex]\frac{180-56}{2}[/tex] = [tex]\frac{124}{2}[/tex] = 62°

200x3=600

50x3=150

600+150=750

750

The smallest value of the function f(x₁, x₂) = x₁ + x₂ on the disk D with a radius of 1 is -√2, and the largest value is √2. The relative change in the smallest value, expressed in percent, can be calculated if the radius of the disk decreases to 0.99.

a) The problem can be formulated as an optimization problem with constraints. We want to find the smallest and largest values that the function f(x₁, x₂) = x₁ + x₂ achieves on the set D, which is defined as the disk with radius r = 1, i.e., D = {(x₁, x₂) ∈ ℝ² | x₁² + x₂² < 1}.

To find the smallest value, we can minimize the function f subject to the constraint that (x₁, x₂) is within the disk D. Mathematically, this can be written as:

Minimize: f(x₁, x₂) = x₁ + x₂

Subject to: x₁² + x₂² < 1

To find the largest value, we can maximize the function f subject to the same constraint. Mathematically, this can be written as:

Maximize: f(x₁, x₂) = x₁ + x₂

Subject to: x₁² + x₂² < 1

b) To find the points at which the function f achieves the maximum and minimum on the set D, we can analyze the problem. The function f(x₁, x₂) = x₁ + x₂ represents a plane with a slope of 1.

Considering the constraint x₁² + x₂² < 1, we observe that it represents a circle with radius 1 centered at the origin.

Since the function f represents a plane with a slope of 1, the maximum and minimum values occur at the points on the boundary of the disk D where the plane is tangent to the disk. In other words, the maximum and minimum values occur at the points where the plane f(x₁, x₂) = x₁ + x₂ is perpendicular to the boundary of the disk.

Considering the disk D: x₁² + x₂² < 1, we can see that the boundary of the disk is x₁² + x₂² = 1 (the equation of a circle).

At the boundary, the gradient of the function f(x₁, x₂) = x₁ + x₂ is parallel to the normal vector of the boundary circle. The gradient of f is (∂f/∂x₁, ∂f/∂x₂) = (1, 1), which represents the direction of steepest ascent of the function.

Thus, at the points where the plane f(x₁, x₂) = x₁ + x₂ is tangent to the boundary circle, the gradient of f is parallel to the normal vector of the circle. Therefore, the gradient of f at these points is proportional to the vector pointing from the origin to the tangent point.

To find the tangent points, we can use the fact that the tangent line to a circle is perpendicular to the radius at the point of tangency. The radius of the circle D is the vector from the origin to any point (x₁, x₂) on the boundary, which is (x₁, x₂).

So, the tangent points occur when the gradient vector (1, 1) is proportional to the radius vector (x₁, x₂), which means:

1/1 = x₁/1 = x₂/1

Simplifying, we get:

x₁ = x₂

Substituting this back into the equation of the boundary circle, we have:

x₁² + x₂² = 1

x₁² + x₁² = 1

2x₁² = 1

x₁² = 1/2

Taking the positive square root, we get:

x₁ = √(1/2)

Since x₁ = x₂, the corresponding values are:

x₂ = √(1/2)

Thus, the points where the function f achieves the maximum and minimum on the set D are (x₁, x₂) = (√(1/2), √(1/2)) and (x₁, x₂) = (-√(1/2), -√(1/2)).

Plugging these values into the function f(x₁, x₂) = x₁ + x₂, we get:

f(√(1/2), √(1/2)) = √(1/2) + √(1/2) = 2√(1/2) = √2

f(-√(1/2), -√(1/2)) = -√(1/2) - √(1/2) = -2√(1/2) = -√2

Therefore, the largest value of f is √2, and the smallest value of f is -√2.

c) Denoting the smallest value as fin = -√2, we can find the relative change in fin expressed in percent if the radius of the disk decreases to D = {(x₁, x₂) ∈ ℝ² | x₁² + x₂² ≤ 0.99}.

To calculate the relative change, we can use the formula:

Relative Change = (New Value - Old Value) / Old Value * 100

The new value of fin, denoted as fin', can be found by minimizing the function f subject to the constraint x₁² + x₂² ≤ 0.99.

Solving the minimization problem, we find the new smallest value fin' on the set D with a radius of 0.99.

Comparing fin' to fin, we can calculate the relative change:

Relative Change = (fin' - fin) / fin * 100

By solving the new minimization problem, you can find the new smallest value fin' and calculate the relative change using the formula provided.

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Answer:

a)  2.7 sec

b)  2.6 sec

c)  30.3 ft,  1.3 sec

Step-by-step explanation:

graphed the equation and determined answers from the curve

Answer:

24

Step-by-step explanation:

6 ÷ 1/4 = 6 × 4 = 24

Answer:

24

Step-by-step explanation:

Answer:

The correct answer in each case is:

Step-by-step explanation:

First, to calculate the surface area or the volume you must have all the measures in the same units, for the exercise we're gonna use centimeters and after we can replace the units in the answer if we need, then:

Now, to obtain the surface area of the triangle we're gonna use the next formula:

And we replace the values in centimeters:

To obtain this same value now in square milimeters, you must know:

Now, you must multiply:

To obtain this value now in [tex]m^{2}[/tex], you must know:

You must divide:

By last, to obtain the volume of the piece of cake, you can use the next formula:

And we replace the surface area in [tex]cm^{2}[/tex] because the answer must be in [tex]cm^{3}[/tex]:

Answer:

[tex]8.71*10^{-3}[/tex]

Step-by-step explanation:

Moving the decimal point 3 spots to the right, we get 8.71, which shows that 0.00871 is equal to 8.71*10^-3 in scientific notation

Answer:

Step-by-step explanation:

0.00871 written in scientific notation is 8.71 x 10^(-3).

hope it helps!

Answer: 2 2/3

Step-by-step explanation:

Answer:

2 2/3

Step-by-step explanation:

Answer:

Step-by-step explanation

Her bank account decreased by 3 times.

Please let me know if this helps you!

Using chain rule the derivative for the function y = -4xln(x + 12) is -4ln(x + 12) - 4x / (x + 12).

To find the derivative of the given function y = -4xln(x + 12), we can use the product rule and the chain rule.

The product rule states that for two functions u(x) and v(x), the derivative of their product is given by:

(d/dx)(u(x)v(x)) = u'(x)v(x) + u(x)v'(x)

In this case, u(x) = -4x and v(x) = ln(x + 12). Let's calculate their derivatives:

u'(x) = -4

v'(x) = 1 / (x + 12)

Applying the product rule, we have:

(d/dx)(-4xln(x + 12)) = (-4)(ln(x + 12)) + (-4x)(1 / (x + 12))

Simplifying further:

= -4ln(x + 12) - 4x / (x + 12)

Therefore, the derivative of y = -4xln(x + 12) is -4ln(x + 12) - 4x / (x + 12).

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The question is -

Find the derivative of the given function.

y = -4xln(x + 12)

A. 3x / x + 12 + 3ln(x+12)

B. 3x / x + 12 - 3ln(x+12)

C. - (3x / x + 12) - 3ln(x+12)

D. - (3x / x + 12) + 4ln(x+12)

The correlation coefficient is:r = -0.332 / (0.683 × 0.566) = -0.994

Correlation Coefficient The correlation coefficient, denoted by r, is a statistical measure of the strength of the relationship between two quantitative variables.

It is always between -1 and 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation at all.

In this problem, we have the joint probability function for X1 and X2 as follows:

P(0,0) = 0.06P(2,0) = 0.20P(1,0) = 0.14P(2,1) = 0.30P(1,1) = 0.10P(2,2) = 0.20

The probability of two calls and one order is given as 0.30. Thus:P(2,1) = 0.30

Now, let us find the marginal probabilities of X1 and X2.P(X1 = 0) = P(0, 0) + P(0, 1) + P(0, 2) = 0.06 + 0 + 0 = 0.06P(X1 = 1) = P(1, 0) + P(1, 1) + P(1, 2) = 0.14 + 0.10 + 0 = 0.24P(X1 = 2) = P(2, 0) + P(2, 1) + P(2, 2) = 0.20 + 0.30 + 0.20 = 0.70Similarly,P(X2 = 0) = P(0, 0) + P(1, 0) + P(2, 0) = 0.06 + 0.14 + 0.20 = 0.40P(X2 = 1) = P(0, 1) + P(1, 1) + P(2, 1) = 0 + 0.10 + 0.30 = 0.40P(X2 = 2) = P(0, 2) + P(1, 2) + P(2, 2) = 0 + 0 + 0.20 = 0.20

The expected values of X1 and X2 are:

E(X1) = 0 × 0.06 + 1 × 0.24 + 2 × 0.70 = 1.64

E(X2) = 0 × 0.40 + 1 × 0.40 + 2 × 0.20 = 0.80

Let us now find the expected value of X1X2:

E(X1X2) = 0 × 0.06 + 1 × 0.00 + 2 × 0.30 + 0 × 0.14 + 1 × 0.10 + 2 × 0.20 = 1.14

Thus, the covariance of X1 and X2 is:Cov(X1, X2) = E(X1X2) - E(X1)E(X2) = 1.14 - 1.64(0.80) = -0.332

Finally, the correlation coefficient is given as

r = Cov(X1, X2) / (σ(X1)σ(X2))

Where σ(X1) is the standard deviation of X1 and σ(X2) is the standard deviation of X2.

Let us find the standard deviations of X1 and X2:

Variance of X1:Var(X1) = E(X1^2) - [E(X1)]^2 = 0^2(0.06) + 1^2(0.24) + 2^2(0.70) - (1.64)^2 = 0.4676

Standard deviation of X1:σ(X1) = √Var(X1) = √0.4676 = 0.683

Variance of X2:Var(X2) = E(X2^2) - [E(X2)]^2 = 0^2(0.40) + 1^2(0.40) + 2^2(0.20) - (0.80)^2 = 0.3200

Standard deviation of X2:σ(X2) = √Var(X2) = √0.3200 = 0.566

Thus, the correlation coefficient is:r = -0.332 / (0.683 × 0.566) = -0.994

Therefore, the correlation coefficient is very close to -1.

This means that there is a very strong negative correlation between the number of calls and the number of orders placed. This can be interpreted as follows: As the number of calls increases, the number of orders placed decreases, and vice versa.

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Answer:

9

Step-by-step explanation:

Answer:

9 square meter

Step-by-step explanation:

1/2xbasexheight

=1/2x6x3

=9

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The reference angles are in the first, second, third, and fourth is 78°, 102°, 258°, and 282° respectively.

the angle between the terminal side of the angle and the x-axis.

For the first quadrant:

The reference angle = 258 - 180 = 78°

For the second quadrant:

= 180 - 78 = 102°

For the third quadrant:

= 78 + 180

= 258°

For the fourth quadrant:

= 360- 78

= 282°

Thus, the reference angles are in the first, second, third, and fourth is 78°, 102°, 258°, and 282° respectively.

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Answer:

7.2

Step-by-step explanation:

Answer:

I dont think you realize you posted the answer...

Step-by-step explanation:

7.2

Answer:

260 minutes > 4.25 hours

Step-by-step explanation:

1h=60 min.

0.25 h=¼h=¼*60min=15min.

4.25h=4h+0.25h=60*4+15min=240+15=255min

260>255

Answer:

60+60+60+60=240

240/4=4,25

=4,25

Answer:

The answers are

x=5

y=12

z=13

Step-by-step explanation:

let the numbers be x,y,z

[tex] \frac{x + y + z}{3} = 10[/tex]

[tex]y = 12[/tex]

[tex]z - x = 8[/tex]

z=8+x

x+12+x+8/3=10

2x+20/3=10

2x+20=30

2x=30-20

2x=10

divide both sides by 2

2x/2=10/2

x=5

z=8+5

z=13

The specific solution to the given ODE with the initial conditions is:

y(t) = (8.5π - 8.5t) [tex]e^{(-2t)[/tex] + 8.5(t - π)

To solve the given ordinary differential equation (ODE) with the initial conditions, we can use the method of undetermined coefficients.

The characteristic equation for the homogeneous part of the ODE is:

r² + 4r + 4 = 0

Solving this quadratic equation, we find a repeated root:

(r + 2)² = 0

r + 2 = 0

r = -2

Since we have a repeated root, the general solution to the homogeneous part is:

[tex]y_{h(t)[/tex]= (C₁ + C₂t) [tex]e^{(-2t)[/tex]

Next, we need to find a particular solution to the non-homogeneous part of the ODE. We assume a particular solution in the form:

[tex]y_{p(t)[/tex] = A(t - π)

Taking the derivatives:

[tex]y'_{p(t)[/tex]  = A

[tex]y''_{p(t)[/tex] = 0

Substituting these derivatives into the ODE:

0 + 4A + 4A(t - π) = 68(t - π)

Simplifying:

8A(t - π) = 68(t - π)

8A = 68

A = 8.5

Therefore, the particular solution is:

[tex]y_{p(t)[/tex] = 8.5(t - π)

The general solution to the ODE is the sum of the homogeneous and particular solutions:

[tex]y(t) = y_{h(t)} + y_{p(t)[/tex]

= (C₁ + C₂t) [tex]e^{(-2t)[/tex] + 8.5(t - π)

To find the values of C₁ and C₂, we apply the initial conditions:

y(0) = 0

0 = (C₁ + C₂(0)) [tex]e^{(-2(0))[/tex] + 8.5(0 - π)

0 = C₁ - 8.5π

C₁ = 8.5π

y'(0) = 0

0 = C₂ [tex]e^{(-2(0))[/tex] + 8.5

0 = C₂ + 8.5

C₂ = -8.5

Therefore, the specific solution to the given ODE with the initial conditions is:

y(t) = (8.5π - 8.5t)  + 8.5(t - π)

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Answer:

B. 37.5

Step-by-step explanation:

100/24 = 4.1666666667

4.1666666667*9 = 37.5

Answer:

Your answer should be C.

Step-by-step explanation:

In order to make 150% you need a whole which represents the 100%. Which leaves B out of the question. A Is not close to half of a bar, which you can also eliminate. C and D are somewhat the same but it has to have the same amount of boxes shaded and unshaded, in this case D is 4 shaded and 2 unshaded which is wrong. So, your answer is C because there is 3 shaded and unshaded boxes in the model, hope this helps!

The diagram that represents 150%​ should be C.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

In order to make 150% we need a whole which represents the 100%. Which leaves B out of the question.

Option A Is not close to half of a bar, which we can also eliminate.

Option C and D are somewhat the same but it has to have the same amount of boxes shaded and unshaded,

In this case D is 4 shaded and 2 unshaded which is wrong.

Therefore, the answer is C because there is 3 shaded and unshaded boxes in the model.

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Answer:

A= 30

B= 24.3

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

To find the range, find the difference between the largest value and the smallest value.

544 - 460 = 84

Answer:

If both expressions have the same value after substituting and simplifying two different values for the variable, then they are  

✔ equivalent

.

!Step-by-step explanation:

hop3 it helped

Answer:

The percent of the air ticket went up 148%  plus the baggage fee would be 168%. The new total is 420$

Step-by-step explanation:

The number of primes up to 250 is 54.

To find the number of primes up to 250, we need to check each number up to 250 to determine whether it is prime or not. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself.

We can use a simple algorithm to determine whether a number is prime or not. We start by checking if the number is divisible by 2. If it is divisible by 2, then it is not prime unless it is 2 itself. If the number is not divisible by 2, we check if it is divisible by any odd numbers starting from 3 up to the square root of the number.

Applying this algorithm to each number up to 250, we can count the number of primes. By doing so, we find that there are 54 prime numbers up to 250.

Therefore, the main answer is that there are 54 primes up to 250.

Note: The explanation provided assumes that by "Primitives," you meant prime numbers.

The second part of the question.

Remainder when "zo" is divided by 11:

To find the remainder when "zo" is divided by 11, we need to assign numerical values to the letters and then perform the division.

In this case, let's assign the values as follows:

z = 26

o = 15

Now, we calculate the value of "zo":

zo = 26 * 10 + 15 = 265

To find the remainder when 265 is divided by 11, we perform the division:

265 ÷ 11 = 24 remainder 1

Therefore, the remainder when "zo" is divided by 11 is 1.

Remainder when "ah!" is divided by 37:

To find the remainder when "ah!" is divided by 37, we assign numerical values to the letters and then perform the division.

In this case, let's assign the values as follows:

a = 1

h = 8

Now, we calculate the value of "ah!":

ah! = 1 * 10 + 8 = 18

To find the remainder when 18 is divided by 37, we perform the division:

18 ÷ 37 = 0 remainder 18

Therefore, the remainder when "ah!" is divided by 37 is 18.

Note: The explanation assumes that the letters in "zo" and "ah!" represent their corresponding positions in the English alphabet (e.g., a = 1, b = 2, etc.).

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Answer:

its in there

Step-by-step explanation:

Answer: Solve the Inequality for h

Solve for h

Graph

Convert to Interval Notation

Evaluate

Write in y=mx+b Form

Find the Exact Value

Solve the Absolute Value Inequality for h

Convert to Set Notation

Plot

Write in Slope-Intercept Form

Solve the Rational Equation for h

Simplify

Add

Solve by Factoring

Describe the Transformation

Evaluate the Summation

Find the Absolute Max and Min over the Interval

Find the Product

Convert from Degrees to Radians

Convert to a Decimal

Subtract

Find the Slope

Find the Domain and Range

Find the Derivative - d/dh

Solve Using the Square Root Property

Find the Direction Angle of the Vector

Multiply

Find the Function Rule

Convert to a Simplified Fraction

Find the Area Between the Curves

Solve the Function Operation

Solve the System of Inequalities

Solve for h in Degrees

Find Where Increasing/Decreasing

Find the Maximum/Minimum Value

Write with Rational (Fractional) Exponents

Evaluate the Limit

Find the Slope and y-intercept

Solve by Isolating the Absolute Value for h

Find All Complex Solutions

Factor over the Complex Numbers

Find the Intersection

Find the Center and Radius

Convert to Radical Form

Find the Integral

Evaluate Using Summation Formulas

Evaluate Using Scientific Notation

Simplify/Condense

Determine if Linear

Graph Using a Table of Values

Reduce

Rationalize the Denominator

Find the Union

Find the Critical Points

Solve for h in Radians

Find the x and y Intercepts

Find the Inverse

Find the Perpendicular Line

Convert from Interval to Inequality

Solve by Completing the Square

Simplify the Matrix

Maximize the Equation given the Constraints

Convert to Regular Notation

Determine if the Relation is a Function

Write in Standard Form

Convert to Trigonometric Form

Split Using Partial Fraction Decomposition

Find the Zeros by Completing the Square

Find the Prime Factorization

Find the Local Maxima and Minima

Find the Quotient

Multiply the Matrices

Factor

There are 80 ways to choose the officers while conforming to University rules.

To determine the number of ways the officers can be chosen while conforming to University rules, we need to consider the different possibilities based on the required conditions.

First, let's consider the positions that must be filled by in-state students and seniors. Since there are 4 in-state seniors and 5 in-state non-seniors, we can select the in-state senior for one position in 4 ways and the in-state non-senior for the other position in 5 ways.

Next, let's consider the remaining position. This can be filled by any of the remaining individuals, which includes 3 out-of-state seniors and 1 out-of-state non-senior. Therefore, there are 4 options for filling the remaining position.

To determine the total number of ways the officers can be chosen, we multiply the number of options for each position: 4 (in-state senior) × 5 (in-state non-senior) × 4 (remaining position) = 80.

Hence, there are 80 ways to choose the officers while conforming to University rules.

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