Solve for x. Then, find m∠FDG and m∠GOF. A. x = 24; m∠FDG = 56°; m∠GOF = 106° B. x = 29; m∠FDG = 66°; m∠GOF = 126° C. x = 28; m∠FDG = 64°; m∠GOF = 116° D. x = 27; m∠FDG = 62°; m∠GOF = 118°

Answer:

P [ Z < 66 ]  = 35,15 %

Step-by-step explanation:

Normal Distribution

Population mean μ₀  = 75,4

Standard deviation  σ = 5,2

Then:

P [ Z < 66 ]  =  ( 66 - 75,4 ) / 5,2

P [ Z < 66 ]  = - 9,4 / 5,2

P [ Z < 66 ]  = - 1,81

In z-table we look for the reciprocate area for that  z score and find

P [ Z < 66 ]  = 0,3515

P [ Z < 66 ]  = 35,15 %

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

We can solve this equation by isolating the variable x.

First let’s apply the distributive property:

[tex]5(x+3)-12=43\\5\cdot x + 5\cdot3 - 12=43\\5x + 15 - 12 = 43[/tex]

Combine like terms:

[tex]5x + 3 = 43[/tex]

Now we can subtract 3 from both sides:

[tex]5x + 3 - 3 = 43-3\\5x = 40[/tex]

Divide both sides by 5:

[tex]5x\div5 = 40\div5\\x = 8[/tex]

So [tex]x=8[/tex].

Hope this helped!

Answer:

x = 8

Step-by-step explanation:

5(x + 3) – 12 = 43

Add 12 to each side

5(x + 3) – 12+12 = 43+12

5(x+3) =45

Divide each side by 5

5(x+3)/5 = 55/5

x+3 = 11

Subtract 3 from each side

x+3-3 = 11-3

x = 8

Answer:

r=17%

Step-by-step explanation:

P is the investment

A is the targeted amount

t= time (25-18=7 years)

A=P(1+r)^t

30000=10000(1+r)^7

(1+r)^7=30000/10000

r=\root(7)(3)-1

r=0.16993 ≅0.17= 17%

check: A=P(1+r)^t ⇒10000(1+0.17)^7=30012≅30000

Answer:

2.94 seconds.

Step-by-step explanation:

The ball will hit the ground when the height of the ball is 0 meters.

The equation is...

h = 61 - 6t - 5t^2.

-5t^2 - 6t + 61 = 0

5t^2 + 6t - 61 = 0

We can use the quadratic formula to solve.

[please ignore the A-hat; that is a bug]

[tex]\frac{-b ± \sqrt{b^2 - 4ac} }{2a}[/tex], where a = 5, b = 6, and c = -61.

= [tex]\frac{-6 ± \sqrt{6^2 - 4 * 5 * (-61)} }{2 * 5}[/tex]

= [tex]\frac{-6 ± \sqrt{36 - 20 * (-61)} }{10}[/tex]

= [tex]\frac{-6 ± \sqrt{36 + 1,220)} }{10}[/tex]

= [tex]\frac{-6 ± \sqrt{1,256} }{10}[/tex]

= [tex]\frac{-6 ± 35.44009029}{10}[/tex]

Since time cannot be negative, we will not minus the 35.44009029.

(-6 + 35.44009029) / 10 = 29.44009029 / 10 = 2.944009029

That is approximately 2.94 seconds.

Hope this helps!

Answer:

[tex]\boxed{t = 2.94 \ seconds}[/tex]

Step-by-step explanation:

When the ball hits the ground, h = 0

Putting this in the equation:

=> [tex]0 = 61-6t-5t^2[/tex]

=> [tex]61-6t-5t^2 = 0[/tex]

Taking -1 as common

=> [tex]-1(5t^2+6t-61) = 0[/tex]

Dividing both sides by -1

=> [tex]5t^2+6t-61 = 0[/tex]

Using Quadratic Equation:

=>t =  [tex]\frac{-b+ / - \sqrt{b^2-4ac} }{2a}[/tex]

=> [tex]\frac{-6 +/- \sqrt{6^2-4(5)(-61)} }{2(5)}\\\frac{-6 +/- \sqrt{36+1220} }{10}[/tex]

=> t = [tex]\frac{-6 +/- 35.44}{10}[/tex]

Either:

t = [tex]\frac{-6+35.44}{10}[/tex]       OR     t = [tex]\frac{-6-35.44}{10}[/tex]

t = 29.44/10      OR     t = -41.44/10

t = 2.94            OR      t = -4.14

Time can never be negative so t = 2.94 secs

Answer:

28

Step-by-step explanation:

12+[(15-5)]+(9-3)]

PEMDAS

Parentheses first

12+[(10)]+(6)]

Then add

12+10+6

Answer: 28

Step-by-step explanation:

Answer:

x=11/2

Step-by-step explanation:

First we can combine similar terms on the left side. 3x + x is 4x and 20-15 is 5

Now that we have combined them, we are left with 4x+5=27

Subtract 5 on both sides to cancel out the 5.

4x=22

Divide both sides by 4

x=22/4

Simplify

x=11/2

Answer:

[tex] \boxed{\sf x = \frac{11}{2}} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: x: \\ \sf \implies 20 + 3x - 15 + x = 27 \\ \\ \sf Grouping \: like \: terms, \: 20 + 3x - 15 + x = \\ \sf (3x + x) + (20 - 15) : \\ \sf \implies \boxed{ \sf (3x + x) + (20 - 15)} = 27 \\ \\ \sf 3x + x = 4x : \\ \sf \implies \boxed{ \sf 4x} + (20 - 15) = 27 \\ \\ \sf 20 - 15 = 5 : \\ \sf \implies 4x + \boxed{ \sf 5} = 27 \\ \\ \sf Subtract \: 5 \: from \: both \: sides: \\ \sf \implies 4x + (5 - \boxed{ \sf 5}) = 27 - \boxed{ \sf 5} \\ \\ \sf 5 - 5 = 0 : \\ \sf \implies 4x = 27 - 5 \\ \\ \sf 27 - 5 = 22 : \\ \sf \implies 4x = \boxed{ \sf 22} \\ \\ \sf Divide \: both \: sides \: of \: 4x = 22 \: by \: 4 : \\ \sf \implies \frac{4x}{4} = \frac{22}{4} \\ \\ \sf \frac{ \cancel{4}}{ \cancel{4}} = 1 : \\ \sf \implies x = \frac{22}{4} \\ \\ \sf \implies x = \frac{11 \times \cancel{2}}{2 \times \cancel{2}} \sf \implies x = \frac{11}{2} [/tex]

Answer:

Step-by-step explanation:

6x – 3y = 3

–2x + 6y = 14

lets solve by substitution:

1) lets isolate y:

6x–3y=3

-3y=-6x+3

y=(-6x+3)/-3

y=2x-1

2) plug in 2x-1 for y in order to find x:

6x-3(2x-1)=3

6x-6x+3=3

3=3

since x cancels out, it means that there is no solution to this linear system of equations

Answer:

No Solution :)

Step-by-step explanation:

Answer:

first number(x) = 2 second number(y)= 6

Step-by-step explanation:

This is an example of a simultaneous equation.

First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".

x + 2y = 14  (equation 1)

2x + y = 10  (equation 2)

This is solved using the elimination method.

We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.

2x + y = 10 MULTIPLY BY 2

4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)

Now subtract equation 1 from equation 2.

4x - x + 2y - 2y = 20 - 14  (2y cancels out here)

3x = 6

x = 2

Now we substitute our x value into equation 1 to find the value of y.

2 + 2y = 14

2y = 12

y = 6

Hope this has answered your question.

Answer:

6 and 2

Step-by-step explanation:

Let the first number =a

Let the second number =b

A first number plus twice a second number is 14.

Twice the first number plus the second totals 10.

We solve the two equations simultaneously

[tex]a+2b=14 \implies a=14-2b\\$Substitute into the second equation$\\2(14-2b)+b=10\\28-4b+b=10\\-3b=10-28\\-3b=-18\\b=6[/tex]

Recall:

a=14-2b

=14-2(6)

=14-12

a=2

The two numbers are 6 and 2.

Answer:

0.57.

Step-by-step explanation:

57  / 100

We divide 57 by 100:

= 0.57

Answer:

φ = 0.34

Step-by-step explanation:

Given:

total number of observations = N = 100

chi-square test for independence χ2 = (4, N = 100) = 11.73

To find:

phi coefficient φ

Solution:

phi coefficient  φ is computed as:

φ = √( χ2 / n )

   = √ (11.73 / 100 )

   = √0.1173

φ = 0.3425

Answer:

-16

Step-by-step explanation:

I solved it out.

Answer:

its d 16

Step-by-step explanation:

i did the test

Answer:

[tex]Range = 16[/tex]

[tex]Inter\ Quartile\ Range = 6.75[/tex]

[tex]Variance = 20.44[/tex]

[tex]Standard\ Deviation = 4.52[/tex]

Step-by-step explanation:

Given

4, 17, 12, 9, 6, 10, 1, 5, 9, 3

Calculating the range;

[tex]Range = Highest - Lowest[/tex]

From the given data;

Highest = 17 and Lowest = 1

Hence;

[tex]Range = 17 - 1[/tex]

[tex]Range = 16[/tex]

Calculating the Inter-quartile Range

Inter quartile range (IQR) is calculates as thus

[tex]IQR = Q_3 - Q_1[/tex]

Where

Q3 = Upper Quartile and Q1 = Lower Quartile

Start by arranging the data in ascending order

1, 3, 4, 5, 6, 9, 9, 10, 12, 17

N = Number of data; N = 10

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

Calculating Q3

[tex]Q_3 = \frac{3}{4}(N+1) th\ item[/tex]

Substitute 10 for N

[tex]Q_3 = \frac{3}{4}(10+1) th\ item[/tex]

[tex]Q_3 = \frac{3}{4}(11) th\ item[/tex]

[tex]Q_3 = \frac{33}{4} th\ item[/tex]

[tex]Q_3 = 8.25 th\ item[/tex]

Express 8.25 as 8 + 0.25

[tex]Q_3 = (8 + 0.25) th\ item[/tex]

[tex]Q_3 = 8th\ item + 0.25 th\ item[/tex]

Express 0.25 as fraction

[tex]Q_3 = 8th\ item +\frac{1}{4} th\ item[/tex]

[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]

From the arranged data;

[tex]8th\ item = 10[/tex] and [tex]9th\ item = 12[/tex]

[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]

[tex]Q_3 = 10 +\frac{1}{4} (12 - 10)[/tex]

[tex]Q_3 = 10 +\frac{1}{4} (2)[/tex]

[tex]Q_3 = 10 +0.5[/tex]

[tex]Q_3 = 10.5[/tex]

Calculating Q1

[tex]Q_1 = \frac{1}{4}(N+1) th\ item[/tex]

Substitute 10 for N

[tex]Q_1 = \frac{1}{4}(10+1) th\ item[/tex]

[tex]Q_1 = \frac{1}{4}(11) th\ item[/tex]

[tex]Q_1 = \frac{11}{4} th\ item[/tex]

[tex]Q_1 = 2.75 th\ item[/tex]

Express 2.75 as 2 + 0.75

[tex]Q_1 = (2 + 0.75) th\ item[/tex]

[tex]Q_1 = 2nd\ item + 0.75 th\ item[/tex]

Express 0.75 as fraction

[tex]Q_1 = 2nd\ item +\frac{3}{4} th\ item[/tex]

[tex]Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)[/tex]

From the arranged data;

[tex]2nd\ item = 3[/tex] and [tex]3rd\ item = 4[/tex]

[tex]Q_1 = 3 +\frac{3}{4} (4 - 3)[/tex]

[tex]Q_1 = 3 +\frac{3}{4} (1)[/tex]

[tex]Q_1 = 3 +0.75[/tex]

[tex]Q_1 = 3 .75[/tex]

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

Recall that

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR = 10.5 - 3.75[/tex]

[tex]IQR = 6.75[/tex]

Calculating Variance

Start by calculating the mean

[tex]Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}[/tex]

[tex]Mean = \frac{76}{10}[/tex]

[tex]Mean = 7.6[/tex]

Subtract the mean from each data, then square the result

[tex](1 - 7.6)^2 = (-6.6)^2 = 43.56[/tex]

[tex](3 - 7.6)^2 = (-4.6)^2 = 21.16[/tex]

[tex](4 - 7.6)^2 = (-3.6)^2 = 12.96[/tex]

[tex](5 - 7.6)^2 = (-2.6)^2 = 6.76[/tex]

[tex](6 - 7.6)^2 = (-1.6)^2 = 2.56[/tex]

[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]

[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]

[tex](10 - 7.6)^2 = (2.4)^2 = 5.76[/tex]

[tex](12 - 7.6)^2 = (4.4)^2 = 19.36[/tex]

[tex](17 - 7.6)^2 = (9.4)^2 = 88.36[/tex]

Sum the result

[tex]43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4[/tex]

Divide by number of observation;

[tex]Variance = \frac{204.4}{10}[/tex]

[tex]Variance = 20.44[/tex]

Calculating Standard Deviation (SD)

[tex]SD = \sqrt{Variance}[/tex]

[tex]SD = \sqrt{20.44}[/tex]

[tex]SD = 4.52[/tex] (Approximated)

Answer:

9

Step-by-step explanation:

Extend every other side of the hexagon so that a triangle is formed.  Since the hexagon is equiangular, the overall triangle is an equilateral triangle, as well as the smaller triangles in the corners.

The length of the sides of the overall triangle is 7 + 2 + 4 = 13.

Therefore, the other two sides of the hexagon are 5 and 4.

The sum is 5 + 4 = 9.

Answer:

u <= 80

u > 80

Step-by-step explanation:

The happiest would be

Null hypothesis: u <= 80

Alternative hypothesis: u > 80

The correct set of hypotheses for the sample in July is H0: μ ≠ 80 Ha: μ = 80.

The null hypothesis H0 which is also known as the default hypothesis states that there is no relationship between the population parameters.  The alternative hypothesis (H1 ) states that there is a relationship between the population parameters.

To learn more about the null hypothesis, please check: brainly.com/question/4454077

Grant can arrange the songs 720 different ways

The different ways Grant can arrange the 6 songs on the playlist is 720.

The different ways to arrange 'n' number of objects are n!.

The number of songs in the playlist are 6.

Therefore, the number of ways Grant can build the playlist is

[tex]= 6!\\= (6)(5)(4)(3)(2)(1)\\= 720[/tex]

Learn more to arrange a certain number of objects in different ways here: https://brainly.com/question/18076424

#SPJ3

Answer:

Option (C)

Step-by-step explanation:

Measure of the arc BC of a circle A = 60°

Since, measure of an arc is equal to the measure of the central angle that intercepts the arc.

Therefore, m∠A = 60°

Since, measure of the inscribed angle is half of the central angle subtended by the same arc.

Therefore, m∠A = [tex]2\times m(\angle {BDC})[/tex]

60° = 2 × m(∠BDC)

m∠BDC = 30°

Therefore, Option (C) will be the answer.

Answer:

It’s C

Step-by-step explanation:

sum of angles = 10800

measurement of a single angle= 1350

Therefore,

No. of sides = sum of angles / single angle

No of sides = 10800 / 1350

No of sides = 8

Answer:

8 sides.

Step-by-step explanation:

If the sum of the angles is 10,800 degrees, and each angle is 1,350 degrees, the deck will have the number of sides of the sum of the angle measurements divided by each angle's measurements.

10,800 / 1,350 = 1,080 / 135 = 8 sides.

Hope this helps!

Answer:

m = 7; n = 12

Step-by-step explanation:

"a regular n-sided polygon has 5 sides more than a

regular m-sided polygon"

n = m + 5

The sum of the measures of the interior angles is

180(n - 2) for the n-sided polygon and

180(m  2) for the m-sided polygon.

"If the sum of interior angles of the regular

n-sided polygon is twice that of the latter"

180(n - 2) = 2(180)(m - 2)

We have a system of equations with 2 equations.

n = m + 5

180(n - 2) = 2(180)(m - 2)

Simplify the second equation:

n - 2 = 2m - 4

n + 2 = 2m

Substitute m + 5 for n.

m + 5 + 2 = 2m

7 = m

m = 7

n = m + 5 = 7 + 5 = 12

Answer: m = 7; n = 12

Answer:

-3/2

Step-by-step explanation:

Hey there!

Well to find the slope of a line with 2 points we use the following formula,

y2 - y1 / x2 - x1

5 - 2 = 3

-6 - -4 = -2

Slope = -3/2

Hope this helps :)

Answer:

[tex]Slope = -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex](-4, 2) \:(-6,5).\\\\m =\frac{y_2-y_1}{x_2-x_1} \\\\x_1 = -4\\y_1 =2\\x_2 = -6\\y_2 =5\\\\m = \frac{5 -2}{-6-(-4)}\\ m = \frac{3}{-6+4}\\ m = \frac{3}{-2}\\ \\Slope = -\frac{3}{2}[/tex]

Answer:

[tex]\boxed{\sf B \ and \ C}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions to solve.

[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(60)=\frac{5.2}{KL}[/tex]

[tex]\sf KL=\frac{5.2}{sin(60)}[/tex]

[tex]\sf sin(90-60)=\frac{3}{KL}[/tex]

[tex]\sf KL=\frac{3}{sin(90-60)}[/tex]

Answer: -4/3

Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.

So the negative reciprocal of 3/4 is -4/3.

Answer:

80 grams of butter

Step-by-step explanation:

640/2=329

3x320=960

960-880=80

Answer:

The predicted value of y is 504.5.

Step-by-step explanation:

Let be [tex]y = 152 + 12.9\cdot x_{1} + 2.7\cdot x_{2}[/tex], for all [tex]x_{1}, x_{2} \in \mathbb{R}[/tex]. If [tex]x_{1} = 20[/tex] and [tex]x_{2} = 35[/tex], the predicted value of y is:

[tex]y = 152 + 12.9\cdot (20) + 2.7\cdot (35)[/tex]

[tex]y = 504.5[/tex]

The predicted value of y is 504.5.

Answer:

15 pt

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 quarts = 2 pints

From the question we were given 7.5 quarts to to get the desired result multiply 7.5 by 2

Which is 7.5 × 2 = 15 pints

Hope this helps you

Answer: I actually do not know but i know that the answer is A.

Step-by-step explanation:

I'm smart

Step-by-step explanation:

Because the sentence is speaking that he has done already so we will use the past verb ran

Rick says he has ran two miles already

Answer:

b. run

Step-by-step explanation:

Rick says he has run two miles already

It will be "ran" if the sentence had said, "Rick 'ran' two miles already."

BRAINLIST PLS!

Answer:

I NEED POINTS

Step-by-step explanation:

Answer:

x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4

Step-by-step explanation:

1. Need to factor or can use the quadratic formula

2x^2-10x-3=0

a=2, b=-10, c=-3

[-b+-sqrt(b^2-4*a*c)]/(2*a)

[10+-sqrt(100-4*(-200)]/4

[10+- sqrt(300)]/4

x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4

Answer:

wrong thing

Step-by-step explanation:

13 arent shaded of the 20 units

7/20 are shaded, 7X1=7, 2X5=10

Answer:

B

Step-by-step explanation:

B is the only set of ordered pairs to represent a function because it is the only one that has no repeating x values while the others do.