In the figure, AB || DE. Find the measure of Z.​

Answer:

m∠A = 39.5°

Step-by-step explanation:

* Lets revise how to find the measure of an angle by using the cosine rule

- In any triangle ABC

# ∠A is opposite to side a

# ∠B is opposite to side b

# ∠C is opposite to side c

- The cosine rule is:

# a² = b² + c² - 2bc × cos(A)

# b² = a² + c² - 2ac × cos(B)

# c² = a² + b² - 2ab × cos(C)

- To find the angles use this rule

# m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

# m∠B = [tex]cos^{-1}\frac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

# m∠C = [tex]cos^{-1}\frac{a^{2}+b^{2}-c^{2}}{2ab}[/tex]

* Lets solve the problem

∵ a = 14 , b = 17 , c = 22

∵ m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

∴ m∠A = [tex]cos^{-1}\frac{17^{2}+22^{2}-14^{2}}{2(17)(22)}[/tex]

∴ m∠A = [tex]cos^{-1}\frac{289+484-196}{748}[/tex]

∴ m∠A = [tex]cos^{-1}\frac{577}{748}[/tex]

∴ m∠A = 39.5°

Answer:

∠A = 39.52°

Step-by-step explanation:

In Δ ABC,

a = 14, b = 17 and c = 22 then we have to find the measure of ∠A.

Since a² = b² + c² - 2.b.c.cosA [ From cosine law]

(14)² = (17)²+ (22)² - 2(17)(22)cosA

196 = 289 + 484 - (748)cosA

196 = 773 - (748)cosA

748(cosA) = 773 - 196 = 577

cosA = [tex]\frac{577}{748}=0.7714[/tex]

A = [tex]cos^{-1}(0.7714)[/tex]

A = 39.52°

Answer:

y = 6x

Step-by-step explanation:

Find slope

Formula

0 - (-3) = 3

0 - (-1/2) = 1/2

Simplify

3/(1/2) = 6

y = 6x

y-intercept

The line crosses the origin, so the y-intercept is 0.

Answer

y = 6x

Answer:

[tex]y=-4x+2[/tex]

Step-by-step explanation:

Since, the slope intercept form of a line is,

[tex]y=mx+c[/tex]

Here, the given equation is,

[tex]4x=2-y[/tex]

[tex]4x+y=2[/tex]    ( Additive property of equality )

[tex]y=-4x+2[/tex]   ( Subtraction property of equality )

Hence, the equation that represents the equivalent equation of the given equation in slope-intercept form is,

[tex]y=-4x+2[/tex]

First option is correct.

Answer:

Step-by-step explanation:

Answer:

The common ratio is -3

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant called the common ratio

In this problem we have

-2,6,-18,54...

Let

a1=-2, a2=6,a3=-18,a4=54

a2/a1=6/-2=-3

a3/a2=-18/6=-3

a4/a3=54/-18=-3

Each term (except the first term) is found by multiplying the previous term by -3

therefore

we have a geometric sequence and the common ratio is -3

Answer:

1) 0.0008306

2) 0.00008306

3) 0.000008306

4) 0.0000008306

Step-by-step explanation:

Please mark me the brainliest... . I am sure the answers are correct.

Answer:

0.0008306

0.00008306

0.000008306

0.0000008306

Step-by-step explanation:

0.008306 ÷ 10 = 0.0008306

0.008306 ÷ 100 = 0.00008306

0.008306 ÷ 1000 = 0.000008306

0.008306 ÷ 10000 = 0.0000008306

Final Answer:

The probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.

Explanation:

To find the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is sufficiently large. In this case, we can assume a sample size of 19 is large enough.

Given:
- Population mean (μ) = 98.20°F
- Population standard deviation (σ) = 0.62°F
- Sample size (n) = 19
- Target sample mean (X) = 98.50°F

We need to do the following steps:

1. Calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.
  SEM = σ / √n

2. Calculate the Z-score for the sample mean of 98.50°F. The Z-score represents how many standard errors the value is away from the population mean.
  Z = (X - μ) / SEM

3. Use the Z-score to find the area to the left of it on the standard normal distribution, which represents the probability that the sample mean is less than 98.50°F.

Let's calculate each step:

1. Calculate SEM:
  SEM = σ / √n
      = 0.62 / √19
      ≈ 0.62 / 4.3589
      ≈ 0.1422

2. Calculate Z-score:
  Z = (X - μ) / SEM
    = (98.50 - 98.20) / 0.1422
    ≈ 0.30 / 0.1422
    ≈ 2.1095

3. Lastly, to find the probability that the sample mean is less than 98.50°F, we look up the Z-score in the standard normal distribution table (Z-table), use statistical software, or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.

A Z-score of 2.1095 corresponds to a probability of about 0.9826 (using Z-table or a calculator).

Therefore, the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.

Among the options given, the closest to 0.9826 is 0.9826 itself. Hence, that is the correct answer.

Answer:

264 unit^2.

Step-by-step explanation:

The lateral area  is the sum of the 2 sides of area 5*11 and the 2 sides of area 7^11.

That would be 2 * 5 * 11 + 2*7*11

=  264 unit^2.

For this case we have that by definition, the lateral area of a prism is given by:

[tex]LA = 2ac + 2bc[/tex]

Where:

a: It is the height

b: It is the width

c: It's the long

According to the figure we have:

[tex]a = 5 \ units\\b = 7 \ units\\c = 11 \ units[/tex]

Substituting:

[tex]LA = 2 * 5 * 11 + 2 * 7 * 11\\LA = 110 + 154\\LA = 264[/tex]

Finally, the lateral area of the prism is [tex]264 \ units ^ 2[/tex]

ANswer:

Option B

Answer:

Its 7.7, 7, 0.6, -0.7

the name of the plane is C. plane EGF

Check the picture below.

Answer:

[tex]\frac{2.5}{100}=0.025\:or\:2.5\%[/tex]

Step-by-step explanation:

In step 4.

Weston made a mistake when he divided 2.5 by 100. He wrote it as he had multiplied 2.5 by 10 instead of moving the point back two decimals places to the left.

In the Step 4:

[tex]\frac{2.5}{100}= 0.025\:or\:2.5\:\%[/tex]

This can be verified by dividing 1 over 40, that'll  give us 0.025

Answer:

k=9

Step-by-step explanation:

First find r=22/20=1.1

The sum of the first k terms formula is a1•(1-r^k)/(1-r)

a1=20 and the sum is 271.59

Now plug in these values in the formula and find k.

271.59=20(1-1.1^k)/(1-1.1)

When you simplify this equation, you will get k=ln(2.358)/ln(1.1)

k=9

Answer:

multiplicity of 1

Step-by-step explanation:

Given the roots of an equation are

x = - 4 ← multiplicity 1

(x + 4)² = 0

x + 4 = 0 or x + 4 = 0 , hence

x = - 4 or x = - 4 , that is

x = - 4 ← with multiplicity 2

(x + 4)³ = 0

has roots x = - 4 with multiplicity 3

The multiplicity is determined by the exponent the factor is raised to

Answer:

Total overripe fruit = 48

Step-by-step explanation:

Step 1: Assume the value of oranges

Let oranges be x

Oranges = x

Apples = 32 + x

Overripe oranges = 3/5 of oranges

                              = 3x/5

Overripe apples = 1/3 of apples

                           = 1/3 (32 + x)

Step 2: Find x (oranges)

Number of overripe apples and number or overripe oranges are equal.

3x/5 = 1/3 (32 + x)

3 (3x) = 5(32 + x)

9x = 160 + 5x

4x = 160

x = 40

Step 3: Find the total number of overripe fruit.

Total overripe fruit = Overripe apples + Overripe oranges

Total overripe fruit = 1/3 (32 + x) + 3x/5

Total overripe fruit = 1/3 (32 + 40) + 3(40)/5

Total overripe fruit = 24 + 24

Total overripe fruit = 48

!!

Answer:

A. By SAS only

Step-by-step explanation:

Side Side Side postulate (SSS) states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In triangles ABC and AED:

So, SAS postulate can be applied.

SSS postulate cannot be applied, because it is not given that sides AB and AE are conruent.

Answer:

ΔABC and ΔAED are congruent to each other by SAS rule.

Step-by-step explanation:

We are given a figure in the question.

The figure shows that:

AC = AD, BC = ED, ∠BAC = ∠EAD

We are also given that triangle BCA is congruent to triangle EDA.

Now, we need to prove that triangle ABC is congruent to triangle AED.

We will use SAS criterion of congruence.

In ΔABC and ΔAED,

AC = AD, ∠BAC = ∠EAD, , BC = ED( all given in the figure)

Hence, the two triangles are congruent to each other by SAS rule.

Answer:

7c^2d-7c+4d-10

Step-by-step explanation:

Start off with the term that has c^2 in it. 5c^2d + 2C = 7c^2d, then since you have multiple choice, the d value differs between the two answer choices that have 7c^2d so you can do +3d +d to get +4d to get the fourth answer choice.

To check your work, you can add/subtract each term to see if you get 7c^2d-7c+4d-10

it's d, since the area of a circle is radius squared times pi

3.14×5^2= 78.4

Final answer:

To find the mean absolute deviation (MAD) for the data set, calculate the mean, subtract it from each data value to find deviations, take the absolute values, and then find their mean. The MAD for the data set 12, 17, 16, 9, 18, 10, 9 is approximately 3.43.

Explanation:

To find the mean absolute deviation (MAD) for a given data set, we follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data value to find the deviations.

Take the absolute value of each deviation.

Find the average of these absolute values to determine the MAD.

The data set provided is: 12, 17, 16, 9, 18, 10, 9. First, let's calculate the mean:

(12 + 17 + 16 + 9 + 18 + 10 + 9) / 7 = 91 / 7 = 13

Next, we'll find the absolute deviations from the mean:

|12 - 13| = 1

|17 - 13| = 4

|16 - 13| = 3

|9 - 13| = 4

|18 - 13| = 5

|10 - 13| = 3

|9 - 13| = 4

Lastly, we calculate the mean of these absolute values:

(1 + 4 + 3 + 4 + 5 + 3 + 4) / 7 = 24 / 7 ≈ 3.43

The mean absolute deviation of the data set is approximately 3.43.

Final answer:

The mean absolute deviation of the data set is calculated by finding the mean, determining the absolute deviation of each value from the mean, and then taking the mean of those deviations. For this set, the mean absolute deviation is 3.43.

Explanation:

To find the mean absolute deviation, we follow these steps:

First, we calculate the mean of the data set: (12 + 17 + 16 + 9 + 18 + 10 + 9) ÷ 7 = 91 ÷ 7 = 13.

Next, we find the absolute deviation of each data point from the mean:

Add these absolute deviations: 1 + 4 + 3 + 4 + 5 + 3 + 4 = 24.

Finally, we find the mean of these absolute deviations: 24 ÷ 7 = 3.43 (rounded to the nearest hundredth).

The mean absolute deviation for the data set is 3.43.

Answer:

1408 min.

Step-by-step explanation:

8 × 176 = 1408.

Answer:

1408

Step-by-step explanation:

Answer:

total cost= 16v+24p

Step-by-step explanation:

One set 4v+6p

Multiply the. expression by 4 because we are buying 4 sets

4v+6p

*4. *4

16v+24p

Answer:

(4v + 6p)4 = n

Step-by-step explanation:

If 1 set is

4v + 6p,

Then multiply it by 4 to get the total cost of 4 sets. Since there is so price for 1 set, we could use n for the missing total cost.

Answer:

(1)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

We are looking for an equation of the form

y = 4x ± c ( since slope m = 4)

The only equation which fits the description is

y = 4x - 3 → (1)

Answer:

Height and base are both 12 in

Step-by-step explanation:

Formula area triangle: area = (height * base) /2

Since for the first triangle height and base are the same we will call is x.

The area for the first triangle is

area = (x^2) /2 = 0.5x^2

The new triangle area is

first triangle - 36 = ((x/2) * x)/2

0,5x^2 - 36 = (0,5x * x)/2

0,5x^2 - 36 = (0,5x^2)/2

0,5x^2 - 36 = 0,25x^2

0,25x^2 = 36

x^2 = 144

X = square root (144) = 12 in

Answer: I know you prob don't need this answer anymore but this is for the people who look it up and need it.

Step-by-step explanation:

It's 2.1*10^-3

[tex]2.1 \times 10^{-3[/tex] is the scientific notation of the given number.

To write in scientific notation,

So, in scientific notation, 0.0021 is written as [tex]2.1 \times 10^{-3[/tex].

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ6

Answer:

[tex]\large\boxed{V=(157.5+27.648\pi)\ yd^3}[/tex]

Step-by-step explanation:

We have the rectangular prism and the cone.

The formula of a volume of

1) a rectangular prism

[tex]V=lwh[/tex]

l - length

w - width

h - height

2) a cone

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have:

1)

l = 7yd, w = 5yd, h = 4.5yd

Substitute:

[tex]V_R=(7)(5)(4.5)=157.5\ yd^3[/tex]

2)

r = 4.8yd, l = 6yd

l - slant height

Use the Pythagorean theorem to calculate H :

[tex]H^2+r^2=l^2[/tex]

Substitute:

[tex]H^2+4.8^2=6^2[/tex]

[tex]H^2+23.04=36[/tex]           subtract 23.04 from both sides

[tex]H^2=12.96\to H=\sqrt{12.96}\\\\H=3.6\ yd[/tex]

Calculate the volume:

[tex]V_C=\dfrac{1}{3}\pi(4.8)^2(3.6)=\dfrac{82.944}{3}\pi=27.648\pi\ yd^3[/tex]

The volume of the composite solid:

[tex]V=V_R+V_C[/tex]

Substitute:

[tex]V=(157.5+27.648\pi)\ yd^3[/tex]

Answer:

(5/2 ,  3/2)

or

(2.5  , 1.5)

(These are the same point; just one is in fraction form and the other in decimal)

Step-by-step explanation:

I could be wrong but I think you want to solve the system

x+y=4

x-y=1

The cool thing about this system it is already set up for elimination (some people call it linear combination).  This means when you add the equations together, a variable will get eliminated allowing you to solve for the other.

x+y=4

x-y=1

----------Add equations.

2x+0=5

2x    =5

 x     =5/2

 x     =2.5

So plug in your x into either one of the equations and solve for y.

x+y=4

2.5+y=4

y=4-2.5

y=1.5

So the solution is (2.5 , 1.5)  or (5/2, 3/2).

Answer:

A) x greater than or equal to −3

Step-by-step explanation:

We have the following inequality:

7 − 9x − (x + 12) ≤ 25

Solving the inequation, we have:

7 − 9x − x - 12 ≤ 25

-10x ≤ 30

-x ≤ 3

x≥-3

Therefore the result is option A) x greater than or equal to −3

Answer:

B.

Step-by-step explanation:

7-9x - (x+12) ≤ 25

7 - 9x - x - 12 ≤ 25

-10x - 5 ≤ 25

-10x ≤ 25 +5

x ≥ 30/-10

x ≥ -3.

So, the incorrect answer is B.

Answer:

1/6

Step-by-step explanation:

(1/2)/3

To solve, note that there are 2 denominators in all. To solve, multiply the denominators together:

(1/2)/3 = 1/(2 * 3) = 1/6

1/6 is your answer.

~

Answer:

0.16

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact form: 1/6

Decimal form: 0.16

Answer:

2.5 gallons

Step-by-step explanation:

We need to go 100 miles

Write the proportion

Picking a point on the graph (40 miles, 1 gallon)

100 miles         40 miles

-------------- = -------------

x gallons         1 gallon

Using cross products

100 * 1 = 40 *x

Divide each side by 40

100/40 = 40x/4

2.5 =x

We need 2.5 gallons to go 100 miles

Answer: Based on the graph, the car requires 2.5 gallons of fuel to travel 100 miles.

Look at the picture below for help. The blue dot represents were the two points meet. We are trying to figure out how many gallons are for the 100 miles, 100 miles would be on the side that says distance (miles). That is were you start. Find point 100 on the distance (miles) side and just draw a straight line, stopping when you hit the black line on the graph. Once done, draw another line going straight down from the black line, and you get your answer of 2.5

Answer: 2.5

Hope it helps!

Answer:

Option B

Step-by-step explanation:

Given:

total No. of students liking peas= 78

total no. of male students= 100

total number of students= 200

no. of male students liking peas= 42

Now we need to find are liking peas and being male independent or dependent events

P(likes peas)= 78/00

                    =0.39

                    =39%

P(likes peas/male) = 42/100

                                = 42%

as the two probabilities are not equal the two events are dependent.

Hence option B is correct: Dependent;

since these probabilities are not equal, the events are dependent!

Answer:

B

Step-by-step explanation:

In the Dependent case  the following relation must be satisfied:

p(a|b) = p(a∩b)/p(b)

Or, in terms of this problem:

p(like peas|male) = p(like peas∩male)/p(male)

The probabilities of this events are:

p(like peas|male) = 42/100 = 42%

p(like peas∩male) = 42/200 = 21%

p(male) = 100/200 = 50%

Therefore, the events are dependent

In the Independent case  the following relation must be satisfied:

p(a|b) = p(a)

or

p(like peas|male) = p(like peas)

p(like peas) = 78/200 = 39%

The equation is not satisfied.

Answer:

m∠1 = 50°

m∠2 =  130°

Step-by-step explanation:

The measure of the angle formed by 2 chords  that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs.

m∠1 = (53+47)/2 = 50°

m∠1 + m∠2 = 180°   ⇒  m∠2 = 180 - m∠1 = 180 - 50 = 130°

The measure of angle 2 (θ2) is given as 312°. To determine the measure of angle 1 (θ1), additional information or context is needed as it is not provided directly in the question or accompanying information.

The question seems to be about finding the measures of angles angle 1 (θ1) and angle 2 (θ2) in a physics context, possibly related to momentum or forces. Given that Ø2 is provided as 312°, we can infer that this is the measurement of angle 2 (θ2). This angle is said to be in the fourth quadrant, which is consistent with the positive counterclockwise definition of angle measurement. For the measure of angle 1 (θ1), there's not enough direct information provided in the question or the reference information to determine its measure. More context or additional data would be necessary to solve for θ1. If the scenario is about a momentum conservation problem, the relationship between angles might be set by the conservation laws for linear momentum in the x and y directions. However, without additional information or clarification from the student's initial query, we would only be speculating on the measure of θ1.

The little red lines on each side of the triangle mean that the sides are all equal.

A triangle that has all 3 sides the same is an equilateral triangle.

Because all the sides are identical all 3 inside angles are also identical.

180 / 3 = 60 degrees

The outside angle which is DEF would equal 180 - the inside angle.

DEF = 180 - 60 = 120.

The answer is D.

Answer:

120°

Step-by-step explanation:

It is an equilateral triangle, so all its sides and internal angles measure the same.

The sum of the internal angles of a triangle must be 180°, so each internal angle measures 60°.

The DEF angle is an external angle of that triangle, we can use the next property:

An external angle of a triangle is the sum of the internal angles opposed to it.

The two opposite angles to DEF are DCE and CDE:

DEF = DCE + CDE = 60 ° + 60 ° = 120°

Another way to find this same result is to notice that DEF + DEC total 180° since they form a straight line, and we know that DEC measures 60°

So:

DEF + DEC = 180 °

DEF = 180 ° - DEC

DEF = 180 ° -60 °

DEF = 120 °