A triangle has an area of 900m2 . If a parallelogram has the same height and base as the triangle, what is the area of the parallelogram?

Answer:

Step-by-step explanation:

In ACB and ECD

AC =~ CE [ Given ]

BC =~ CD [ Given ]

<ACD =~ <ECD [ Vertical angles ]

Hence, ∆ ACB =~ ECD by SAS congruency of triangles.

Then, <B = <D

In ∆ABC , sum of all three angles must be 180°

<A + <B + <C = 180°

plug the values

[tex] 30 + < d \: + 70 = 180[/tex]

Add the numbers

[tex]100 + < d = 180[/tex]

Move constant to R.H.S and change it's sign

[tex] < d = 180 - 110[/tex]

Subtract the numbers

[tex] < d = 80[/tex] °

Hope this helps..

Best regards!!

Answer:

The fraction that this is true for = 7/13

Step-by-step explanation:

From the above question

Let the numerator be represented by a

Let the denominator be represented by b

If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

Cross Multiply

3(a + 5) = 2(b + 5)

3a + 15 = 2b + 10

Collect like terms

3a - 2b = 10 - 15

3a - 2b = -5..........Equation 1

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

Cross Multiply

4(a - 5) = 1(b - 5)

4a - 20 = b - 5

Collect like terms

4a - b = 20 - 5

4a - b = 15..........Equation 2

b = 4a - 15

3a - 2b = -5..........Equation 1

4a - b = 15..........Equation 2

Substitute 4a - 15 for b in equation 1

3a - 2b = -5..........Equation 1

3a - 2(4a - 15) = -5

3a - 8a + 30 = -5

Collect like terms

3a - 8a = -5 - 30

-5a = -35

a = -35/-5

a = 7

Therefore, the numerator of the fraction = 7

Substitute 7 for a in Equation 2

4a - b = 15..........Equation 2

4 × 7 - b = 15

28 - b =15

28 - 15 = b

b = 13

The denominator = b is 13.

Therefore,the fraction which this is true for = 7/13

To confirm

a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

7 + 5/ 13 + 5 = 2/3

12/18 = 2/3

Divide numerator and denominator by of the left hand side by 6

12÷ 6/ 18 ÷ 6 = 2/3

2/3 =2/3

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

7 - 5/13 - 5 = 1/4

2/8 = 1/4

Divide the numerator and denominator of the left hand side by 2

2÷2/8 ÷ 2 = 1/4

1/4 = 1/4

From the above confirmation, the fraction that this is true for is 7/13

Answer:

d.

Step-by-step explanation:

[tex]f(g(x))=3(g(x))^2-12=3(5x+3)^2-12=3(25x^2+30x+9)-12=75x^2+90x+27-12=75x^2+90x+15[/tex]

Answer:

C.I =  0.7608   ≤ p ≤   0.8392

Step-by-step explanation:

Given that:

Let consider a  random sample n = 400 candidates where  320 residents indicated that they voted for Obama

probability [tex]\hat p = \dfrac{320}{400}[/tex]

= 0.8

Level of significance ∝ = 100 -95%

= 5%

= 0.05

The objective is to  develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.

The confidence internal can be computed as:

[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]

where;

[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960

SO;

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]

[tex]=0.8 \pm 1.960 \times 0.02}[/tex]

[tex]=0.8 \pm 0.0392[/tex]

= 0.8 - 0.0392     OR   0.8 + 0.0392  

= 0.7608    OR    0.8392

Thus; C.I =  0.7608   ≤ p ≤   0.8392

Answer:

y= 250( 1-0.21)^x

Step-by-step explanation:

This represents exponential decay

The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.

The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that a population of 250 animals is decreasing at an annual rate of 21%.

p = a x b[tex].^t[/tex]

p = a x (1+r)[tex].^t[/tex]

p = 250 x (1+(-0.21))[tex].^t[/tex]

p = 250(0.79)[tex].^t[/tex]

Note that r = -0.21 is negative to indicate we have exponential decay.

Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.

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Answer:

[tex]\boxed{\sf x - 5 = 10}[/tex]

Step-by-step explanation:

Taking away 5 from x ⇒ subtracting 5 from x

[tex]\large {\sf x - 5[/tex]

Gives 10 ⇒ result is 10

[tex]\large {\sf x - 5 = 10[/tex]

Answer:

I NEED POINTS

Step-by-step explanation:

Answer:

AC = DF

Step-by-step explanation:

The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.

Answer:

Hope it helps <3

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▹ Answer

Use a graphing calculator. Attached is an image.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

9

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

1/5 are towboats

Step-by-step explanation:

In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together

30k + 10k + 10k= 50k

In total there are 50,000 flag vessels

Of those 50,000, 10,000 of them are tow boats

10,000/50,000 can be simplified to 1/5

1/5 are towboats

Answer:

1/5

Step-by-step explanation:

Well to find the fraction we first need to know the total amount of Flag Vessels.

30,000 + 10,000 + 10,000 = 50,000

If there are 10,000 towboats we can make the following fraction.

10,000/50,000

Simplified

1/5

Thus,

the answer is 1/5.

Hope this helps :)

Answer:

Step-by-step explanation:

Given : A right triangle

To do : Solve for x

Solution,

[tex]cos \: 55 = \frac{x}{20} [/tex] ( by definition of cos function, adjacent / hypotenuse )

[tex]0.5736 = \frac{x}{20} [/tex]

multiply both sides of the equation by 20

[tex](0.5736) \times 20 = x[/tex]

Calculate the product

[tex]11.471 = x[/tex]

Swipe both sides of the equation

[tex]x = 11.471[/tex]

Round answer to nearest hundredth

[tex]x = 11.47[/tex]

Hope this helps...

Best regards!!

Answer:

C. 1/8

Step-by-step explanation:

Probability of shooting a goal on a throw is 2/4 = 1/2.

Probability of 3 in a row is (1/2)³ = 1/8.

We are given [tex]\triangle ABC \cong \triangle EFG[/tex]

The order of the letter sequence is important. The letters pair up based on how they are arranged. We see that A and E are the first letters of the sequences. So this means that angles A and E are the same measure

angle A = angle E

3x+20 = 5x-80

3x-5x = -80-20

-2x = -100

x = -100/(-2)

x = 50

Use this x value to find the measure of angle A

angle A = 3x+20

angle A = 3(50)+20

angle A = 150+20

angle A = 170 degrees

Answer:

27

Step-by-step explanation:

Hello,

11011 in base 2 is

1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 in base 10

which is 16 +8+2+1=27

Do not hesitate if you have any question

Answer: 3/50

Step-by-step explanation:

0.06 = 6/100 , 100 would be the denominator because we have two figures after the decimal point. Each figures can also be represented by 10,

Again,

0.06 = 6 × 10-²

Now 0.06 = 6/100

= 3/50.

Therefore, the fractional form = 3/50 in its lowest term.

Answer:

Step-by-step explanation:

Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same

Let's get the slope of both equation. For the first equation;

y=(3a+2)x-2

We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2

Similarly for the second line;

2y=(a-4)x+2

Re-writing in the standard format we will have;

y = (a-4)x/2+2/2

y = (a-4)x/2 + 1

The slope of the second line is (a-4)/2

On equating the slope of both lines to get the value of 'a' we will have;

3a+2 = (a-4)/2

Cross multiplying

2(3a+2) = a-4

6a+4 = a-4

Collecting like terms;

6a-a = -4-4

5a = -8

a = -8/5

Hence the value of a is -8/5

Answer:

2(x^2 + 8x -55)

Step-by-step explanation:

Well to do the box method we first need to simplify the given equation further to,

[tex]2x^2 + 16x - 110\\[/tex],

For this quadratic the box method doesn't work so we can divide everything by 2 make make it

2(x^2 + 8x -55)

Thus,

[tex]2x^2 + 16x - 110\\[/tex] factored is 2(x^2 + 8x -55).

Hope this helps :)

Answer:

1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70

2. Test Statistic : 0.54 , P value : 0.2946

3. Fail to reject null Hypothesis

4. No.

Step-by-step explanation:

1. Null hypothesis is 70% of children receive antibiotics.

Alternative hypothesis is more than 70% of children receive antibiotics.

2. Test statistic is calculated as;

z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]

z = [tex]\frac{0.01}{0.0185}[/tex]

z = 0.54

3. p value is calculated as;

1 - right tailed probability

1 - 0.7054 = 0.2946

Answer:

30.5

Step-by-step explanation:

This sequence is defined by f(n)=6.5 + 4.5

The term inside the parentheses (n) is the value you should input to get an output.

n varies from 0 to infinity

Now to find the fifth term put in mind that 0 is the first term.

This means that f(5) isn't the fifth term. In fact, it's the sixth term. So f(4) is the fifth term.

To find f(4) replace n by 4.

f(4) = 6.5 *4 +4.5 = 26+4.5=30.5

Answer:

[tex]\boxed{ \sf 41.81}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions.

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

[tex]\sf sin(?)=\frac{2}{3}[/tex]

[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]

[tex]\sf ?= 41.81031489...[/tex]

Answer:

[tex]\boxed{41.81}[/tex]

Step-by-step explanation:

∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.

The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).

However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.

Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.

Answer:

15) 2.08m

Step-by-step explanation:

We kow tanA= p/b

Here, A=33°

b=3.2m

Then,

tan33°=p/3.2

0.65=p/3.2

p=0.65*3.2

p=2.08

So, The height of tree is 2.08m

14) 59.58ft

tan50°=p/b

1.19=p/50

p=59.58ft

So, The height of signpost is 59.58ft

In both of these problems, we will be using trigonometry! Remember, SOH-CAH-TOA.

14. x = 13.5950 ft

Visualization of the problem is attached below.

We want to find out the opposite side to the angle, and we know the adjacent side. Therefore, we should use the tangent function.

tan(50) = x / 50

x = tan(50) * 50

x = 13.5950 ft (round off wherever you need)

15. x = 241.0016 m

The visualization of the problem is already given. We know the same information as we need in the previous problems, an angle and an adjacent side, and we want to find the opposite side. Therefore, we should use the tangent function.

tan(33) = x / 3.2

x = tan(33) * 3.2

x = 241.0016 (round off wherever you need)

Hope this helps!! :)

Step-by-step explanation:

A t

eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.

Answer:

A.The school play opens tonight and it is raining.

B.Neva is hungry and she buys a snack from the concession stand.

C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.

D.Luka paints during school and he stains his shirt.

Answer:

3+x

Step-by-step explanation:

sum= addition

a number= a number

Answer:

3+x  

eplanation                                  

Answer:

see details below

Step-by-step explanation:

The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.

a. Determine the amount to be financed.​​​​​​​15a. ___$23450____________

29450 - 6000 = 23450

b. Determine the installment price.​​​​​​​​b. ___$792,22______________

"monthly payment of $792.22"

c. Determine the finance charge.​​​​​​​​c. __$5069.92_______________

A = 792.22

n = 36

finance charge = total paid - amount to be financed

= 36*792.22 - 23450

= 5069.92

Answer:

Step-by-step explanation:

The claim: "Less than 40% of college students graduate with student loan debt."

The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%

If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.

A type I error occurs when the research rejects the null when it is actually true.

Answer:

Hey there!

Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.

Hope this helps :)

Answer:

Option(A) is correct

Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Step-by-step explanation:

The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58

the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:

Highest = 97

Lowest = 71

Range = highest value - Minimum value

Range = 97 - 26 = 71

[tex] Range= 71[/tex]

mean of the data is the summation of all the numbers in the data set divided by the number of given samples.

Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11

= 647/11

[tex]Mean value =58.7[/tex]

Now to find the variance of the data set by using below formular

σ²=[ (xᵢ -mean)²]/n-1

[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10

[tex]Variance=546[/tex]

Now, we will calculate standard deviation by taking square root over variance

σ =√(variance)

σ =√(546)

[tex]Standard deviation= 23.4[/tex]

Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,

Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Answer:   90°

Step-by-step explanation:

As known ∡EGC=(arcEC+arcDF)/2

arcEC+arcDF=70°*2

5x+10+11x+2=140

16x+12=140

16x=128

x=128:16

x=8

So arcDF=11*x+2=11*8+2=90°

The measure of arc DF is 90°.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

Given,  Circle A with chords EF and CD that intersect at point G,

arc EC = 5x + 10°

arc DF = 11x + 2°

∠EGC = 70°

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

so

∠EGC=(1/2)[arc EC+arc DF]

substitute the values

70 = 1/2(5x + 10 + 11x + 2)

70 = 1/2(16x + 12)

140 = 16x + 12

16x = 128

x = 128/16 = 8

so ac DF = 11x + 2

arc DF = 11(8) + 2

arc DF= 88 + 2 = 90°

Hence the value of arc DF is 90°.

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Answer:

(0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

First graph in top row is the answer.

Step-by-step explanation:

The given function is, f(x) = x⁴ - 4x³ + x² + 6x

For zeros of the given function, f(x) = 0

x⁴ - 4x³ + x² + 6x = 0

x(x³ - 4x² + x + 6) = 0

Therefore, x = 0 is the root.

Possible rational roots = [tex]\frac{\pm 1, \pm 2, \pm 3, \pm 6}{\pm1}[/tex]

                                      = {±1. ±2, ±3, ±6}

By substituting x = -1 in the polynomial,

x⁴ - 4x³ + x² + 6x = (-1)⁴ - 4(-1)³+ (-1)² + 6(-1)

                           = 1 + 4 + 1 - 6

                           = 0

Therefore, x = -1 is also a root of this function.

For x = 2,

x⁴ - 4x³ + x² + 6x = (2)⁴ - 4(2)³+ (2)² + 6(2)

                           = 16 - 32 + 4 + 12

                           = 0

Therefore, x = 2 is a root of the function.

For x = 3,

x⁴ - 4x³ + x² + 6x = (3)⁴ - 4(3)³+ (3)² + 6(3)

                           = 81 - 108 + 9 + 18

                           = 0

Therefore, x = 3 is a root of the function.

x = 0, -1, 2, 3 are the roots of the given function.

In other words, (0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

From these points, first graph in top row is the answer.