Hi everyone! I have a quick math question for you guys! Please see the screenshot! Thank you so much! :)

Answer:

14.3cm

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(a^{2}\) + \(7^{2}\) = \(10^{2}\)

\(a^{2}\) + 49 = 100  Subtract 49 from both sides

\(a^{2}\) + 49 - 49 = 100 - 49

\(a^{2}\) = 51

\(\sqrt{a^{2} }\) = \(\sqrt{51}\)

a = 7.14142842854  This is a rounded number.  This is an irrational number.  That means that it never repeats or terminates.  It is like \(\pi\).

We just found the left side of the base of the triangle.  We need to double this to find FG.

7.14142842854 x 2 = 14.2828568571

Round this to 1 decimal place 14.3

Helping in the name of Jesus.

Answer: 14.28 cm

Step-by-step explanation:

So, 10 squared = 7 squared + X squared.

This can be simplified to: 100 = 49 + X squared.

Then, you subtract 49, and are left with 51 = X squared

Then, take the square root if 51, you get approx. 7.14 cm.
since this is an equilateral triangle, the answer will be the same for the second half of the base.
So, 7.14 x 2, 14.28 cm

Answer:

2 ND option

solve and write

Answer:

Since M1 has the higher probability of being in the desired range, we choose M1.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two machines M1, M2 are used to manufacture resistors with a design specification of 1000 ohm with 10% tolerance.

So we need the machines to be within 1000 - 0.1*1000 = 900 ohms and 1000 + 0.1*1000 = 1100 ohms.

For each machine, we need to find the probabilty of the machine being in this range. We choose the one with the higher probability.

M1:

Resistors of M1 are found to follow normal distribution with mean 1050 ohm and standard deviation of 100 ohm. This means that \(\mu = 1050, \sigma = 100\)

The probability is the pvalue of Z when X = 1100 subtracted by the pvalue of Z when X = 900. So

X = 1100

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1100 - 1050}{100}\)

\(Z = 0.5\)

\(Z = 0.5\) has a pvalue of 0.6915.

X = 900

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{900 - 1050}{100}\)

\(Z = -1.5\)

\(Z = -1.5\) has a pvalue of 0.0668

0.6915 - 0.0668 = 0.6247.

M1 has a 62.47% probability of being in the desired range.

M2:

M2 are found to follow normal distribution with mean 1000 ohm and standard deviation of 120 ohm. This means that \(\mu = 1000, \sigma = 120\)

X = 1100

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1100 - 1000}{120}\)

\(Z = 0.83\)

\(Z = 0.83\) has a pvalue of 0.7967.

X = 900

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{900 - 1000}{120}\)

\(Z = -0.83\)

\(Z = -0.83\) has a pvalue of 0.2033

0.7967 - 0.2033 = 0.5934

M2 has a 59.34% probability of being in the desired range.

Since M1 has the higher probability of being in the desired range, we choose M1.

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

A:1,3,5,7,9

b:2,3,5,7,

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Given:

a graph of the inequalities is given.

Find:

we have to find the correct inequalities.

Explanation:

From the graph , it is observed that the value of y > x and y < 4,

Therefore, the correct inequalities are y > x,

y < 4.

Hence, correct option is A.

Answer:

12 rides

Step-by-step explanation:

First, get the total and subtract it from the expenses.

34 - 8.50 - 4.50 = 21

Then divide the answer by how much each ride costs to find the answer

21 ➗1.75 = 12

So Sam can ride 12 rides.

Answer:

Zero(s) of multiplicity one: 11,-9

Zero(s) of multiplicity two: None

Zero(s) of multiplicity three: 5

Step-by-step explanation:

Suppose that we have a polynomial function in the following format:

\(f(x) = a*(x - x_{0})^{m_{0}}*(x - x_{1})^{m^{1}}*...*(x - x_{n})^{m^{n}}\)

The zeros are \(x_{0}, x_{1}, ..., x_{n}\).

The multiplicites are \(m_{0}, m_{1},..., m_{n}\)

In this question:

f(x) = 4(x -11) (x + 9) (x - 5)^3

So

11 is a zero of multiplicity 1

-9 is a zero of multiplicity 1

5 is a zero of multiplicity 3.

So the answer is:

Zero(s) of multiplicity one: 11,-9

Zero(s) of multiplicity two: None

Zero(s) of multiplicity three: 5

Answer:

\(\large\boxed{x = -23}\)

Step-by-step explanation:

6x + 3 = 6x - 20 - x

Subtract 6x from both sides of the equation

3 = -20 - x

Add 20 to both sides of the equation

23 = -x

Multiply both sides of the equation by - 1

(-1)(23) = -x(-1)

x = -23

\(\large\boxed{x = -23}\)

Hope this helps :)

Answer:

A.

Step-by-step explanation:

In this case, on each coordinate point, distance/time = 2.

Anna's average speed during the swimming races as shown in the graph is 2 m/s

An equation is an expression used to show the relationship between two or more numbers and variables.

Anna's average speed can be gotten from the slope of the line. The line pass through (0, 0) and (3, 6), hence:

Slope = (6 - 0) / (3 - 0) = 2 m/s

Anna's average speed during the swimming races as shown in the graph is 2 m/s

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The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

The picture where the red image is the skinniest

Step-by-step explanation:

The graph P(x) denotes the graph of the parent graph for all the functions. And, It includes the vertex of (0,0) and points which are shown below:

x      f(x)

-2      2

-1       1

0       0

1         1

2       2

Now as we can see in the attached figure i.e it changed the function points i.e given below for l(x) = 12P(x)

x      f(x)

-2      24

-1        12  

0        0

1        12

2       24

This depicts that it has a skinner graph that includes redish graph

Answer:

the 4 dimensions

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

Ok first let's put the equation.

-0.2(3x – 25) = -0.1x + 7 (first distribute the -.2 to 3x and -25)

-0.6x + 5 = -0.1x + 7 (subtract 5 on both sides)

-0.6x = -0.1x + 2 (add -0.1x on both sides)

-0.5x = 2 (divide by -0.5 on both sides)

x = -4

Hope this helps!!

The course of the airplane relative to true north is 094°, and the ground speed is 344.2 km/h.

The horizontal and vertical component of the airspeed is calculated as follows;

Vx = 300 cos(30) = 259.8 km/h

Vy = 300 x sin(30) = 150 km/h

The horizontal and vertical component of the wind velocity is calculated as follows;

Vx = 50 cos(60) = 25 km/h

Vy = 50 sin(60) = 43.3 km/h

To find the resultant velocity, we can add the x and y components separately:

Vx = 259.8 km/h  +  25 km/h = 284.8 km/h

Vy = 150 km/h  +  43.3 km/h  = 193.3 km/h

The magnitude of the resultant velocity is calculated as;

V = √(284.8² + 193.3²)

V = 344.2 km/h

The direction of the resultant velocity is calculated as;

θ = arc tan (193.3/284.8)

θ = 34.2⁰

The resultant direction to true north is calculated as;

track = 34.2 + 60 = 94.2°

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Answer:

the first one is (23)

number 7 is ( 34.069)

Step-by-step explanation:

Answer:

105n-25n^2

Step-by-step explanation:

-5(-16+5n-5)

-5(-21+5n)

=105n-25n^2

Answer:

1. 1056.67

2. 29th percentile.

3. 79

4. 77

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean score of 1150, standard deviation of 90

This means that \(\mu = 1150, \sigma = 90\)

1. What is the score for someone in the 15th percentile?

This is X when Z has a p-value of 0.15, so X when Z = -1.037.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.037 = \frac{X - 1150}{90}\)

\(X - 1150 = -1.037*90\)

\(X = 1056.67\)

2. What is the percentile rank of someone with a score of 1100?

This is the p-value of Z when X = 1100. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1100 - 1150}{90}\)

\(Z = -0.555\)

\(Z = -0.555\) has a p-value of 0.29, so 29th percentile.

3. How many students have scores of 1060 or greater?

The proportion is 1 subtracted by the p-value of Z when X = 1060. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1060 - 1150}{90}\)

\(Z = -1\)

\(Z = -1\) has a p-value of 0.1587.

Out of 500:

0.1587*500 = 79

79 is the answer.

4. How many students scored between 1200 and 1250?

The proportion is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1200. So

X = 1250

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1250 - 1150}{90}\)

\(Z = 1.1\)

\(Z = 1.1\) has a p-value of 0.8643.

X = 1200

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1200 - 1150}{90}\)

\(Z = 0.555\)

\(Z = 0.555\) has a p-value of 0.7106

0.8643 - 0.7106 = 0.1537

Out of 500:

0.1537*500 = 77

77 is the answer.

Answer:

The correct choice is option D. y = 2x -12

Step-by-step explanation:

slope of the points (5,-2) and (8,4) is m = 2

y — intercept of the points (5,-2) and (8,4) is b = -12

Now, put it all together, and you'll get :  y = 2x -12

Answer:8

Step-by-step explanation:8x1=8

Answer:

83 degrees

Step-by-step explanation:

79 + 24 = 83

Answer: 5/8

Step-by-step explanation: There are 8 members. Out of 8, there are 5 people's weight that are higher than 135. Therefore the answer is 5/8.

Answer: the awnser is 33 3/4

Step-by-step explanation: im literally doing the same test

The area of a parallelogram can be found by finding the product of its height and base. The area of  the resulting figure is 105/4 sq. ft.

A parallelogram can be defined as a quadrilateral which has equal and parallel opposite sides. The sum of the adjacent angles of a parallelogram is equal to 180° and its opposite angles are equal.

Each side of the square is given 4 1/2 ft,

And the height of each parallelogram 1 1/2 ft.

Now, the area of square is (side)^2 and the area of parallelogram is height × base.

Thus, area of given figure is given as,

Area = (4 1/2)^2 + 2×(4 1/2)×( 1 1/2)

        = 105/4 sq. ft.

Hence, the area of the given figure is 105/4 sq. ft.

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The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

The graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.

If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.

In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

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Answer:

( 2,0)

Step-by-step explanation:

The line crosses the Y intercept at the coordinates at (2,0)

Answer:

the y-intercept of the graph is 2

the ordered pair is (0,2)

Step-by-step explanation:

The y-intercept is the point where the line crosses the "y" line. Ordered pair are written (x,y)  (the x is always in the front)

So, if we look at the "y" line we can see they y point is a 2, and if we look at line "x", the 2 is "above" the point 0 on the line labeled x.

Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Determine if the conditional statement and its converse are true. If a ripe piece of fruit is a strawberry, then it is red

Conditional statement: A ripe piece of fruit is a strawberry

Converse: It is red

Conditional is not always true, because there may be different ripe fruits

The converse is true if conditional is true.

The answer will be A. Neither are true