The base of a triangle is 4 cm greater than the
height. The area is 30 cm. Find the height and
the length of the base
h
The height of the triangle is
The base of the triangle is​

Answer:

The critical region for α= 0.05 is Z > ± 1.645

The calculated value of Z= 1.100

Step-by-step explanation:

The null and alternate hypotheses are given

H0: μ ≤ 43

H1: μ > 43  one tail test

∝= 0.05

n= 29

Standard Deviation= s= 4.1

Mean = μ0 = 44

For one tail test the z value of α= ± 1.645

The critical region for α= 0.05 is Z > ± 1.645

The test statistic is given by

z=μ0-μ/ s/√n

Z= 44-43/4.1/√29

Z= 1/4.1/√29

Z= 1.100

Since the calculated value Z= 1.100 does not  fall in the critical region , We reject H0 and may conclude that the mean number of calls per salesperson per week is not more than 43

Answer:

1/2

Step-by-step explanation:

The probailty of an event A is:

● P(A) = ( outcomes that give A) / (total number of possible outcomes)

Let A be the event in wich we get an even number.

● The sample space is {2,4,6}

So there are 3 possible outcomes that give A .

The six-sided dice has 6 outcomes

● { 1,2,3,4,5,6}

■■■■■■■■■■■■■■■■■■■■■■■■■■

● P(A) = 3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

i took the test

Answer:

  2700 years

Step-by-step explanation:

The exponential function for the fraction remaining is ...

  r(t) = (1/2)^(t/5730)

where r is the remaining fraction and t is the time in years. We can solve for t to get ...

  log(r) = (t/5730)log(1/2)

  t = 5730·log(r)/log(1/2)

For the given r=0.72, the age of the artifact is estimated to be ...

  t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years

Answer:

The same mean  ⇒  the same symmetry axis

Bigger standard deviation major spread

Step-by-step explanation: See Annex

The annex shows two different normal curves:

1.-  N (μ₀ ; σ₁ )

2.- N (μ₀ ; σ₂ )

Where   σ₁  > σ₂

They both have the same symmetry  axis ( they have the same mean and both curves have to be symmetrically related to the mean )

Normal distribution curves spread symmetrically at both sides of the mean, but the wider curve is the one that has the bigger standard deviation.  Standard deviation is a measure of the spread of the curve.

Whenever deviation is high, the data is more dispersed than when deviation is low.

Let the mean be 2.

Let the standard deviation be 0.3 for first graph. The data is more clustered around mean.

Let the standard deviation be 0.6 for second graph. The data is less clustered more dispersed from mean.

For more information, refer this link:

https://brainly.com/question/12421652

Answer:

Step-by-step explanation:

8-2=6

answer is 6

Answer:

2 x 4

Step-by-step explanation:

She need to travel 4 times before she reach the same points again

Answer:

x-y=12

Step-by-step explanation:

Answer:

Step-by-step explanation:

We will use the set notation to solve this question.

let n(U) be the total number of students surveyed = 100

n(M) be the number of student that took math = 34

n(E) be the number of student that took English = 59

n(M∩E) be the number of student that took both classes= 12

n(M∪E)' be the number of student that took neither class = ?

Using the formula n(U) = n(M∪E) + n(M∪E)'

n(M∪E)' = n(U)-n(M∪E)

Before we can get the number of student that took neither class i.e n(M∪E)'  we need to  get n(M∪E).

n(M∪E) = n(M)+n(E)- n(M∩E)

n(M∪E) = 34+59-12

n(M∪E)  = 81

Since n(M∪E)' = n(U)-n(M∪E);

n(M∪E)' = 100-81

n(M∪E)' = 19

Hence 19 students took neither class as a freshmen.

On a number​ line, the coordinates of​ X, Y,​ Z, and W are −7​, −2​, 2​, and 7​, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and

Answer:

5/12

Step-by-step explanation:

(5 * 2^1/4)/4 * 162^1/4) = (5 * 2^1/4)/4 * 3 *2^1/4)

multiply top and bottom by 2^3/4

(5 * 2)/4 * 3 * 2) = 10/24 = 5/12

Answer:

From the given points above, the distance between them is 4 units.

Step-by-step explanation:

In order to find the distance between the two points, we must know the distance formula.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Now, we plug in our numbers from the coordinate points that we are given to their respectful places.

[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]

Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.

[tex]d=\sqrt{(0)^2+(4)^2}[/tex]

Next, solve for the exponents.

[tex]d=\sqrt{0+16}[/tex]

Add the numbers in the radical.  

[tex]d=\sqrt{16}[/tex]

Solve the radical.

[tex]d=4[/tex]

So, the distance  between the two given points is 4 units.

Answer:

Abel receives $60, and Cedric receives $120

Step-by-step explanation:

Let Abel's share = A

Let Cedric's share = C

we are given the following

A + C = 180  - - - - - (1)   (Abel and Cedric will share a total of $180)

[tex]A = \frac{C}{2}\ - - - - - - - (2)[/tex] (Abel will receive half as much as Cedric. )

from equation 2:

[tex]A = \frac{C}{2}\\ C = 2A\ - - - - - - (3)[/tex]

putting this value of C in eqn (3) into eqn (1)

A + (2A) = 180

3A = 180

∴ A = 180 ÷ 3 = 60

to find C, let us replace the value of A in eqn (3) with 60

C = 2A - - - - (3)

C = 2 × 60

C = 120

Therefore, Abel receives $60, and Cedric receives $120

Answer: $12 less.

Step-by-step explanation:

Given: Ms. Cole pays $2 a month  for online banking at her credit union.

In 6 months she will pay = 6 x ($2)

= $12

It means that he balance will be decreased by $12 [as the amount was debited from the balance].

So, the change in the balance of her account if she pays this fee for 6 months = $12 less.

Answer:

.22

Step-by-step explanation:

The number of times a 3 was rolled is 44 out of 200

The experimental probability is  44/200 = .22

The frequency of rolling a 3 was 44.

So... 44/200

After dividing we get 0.22

Therefore, the answer is A

Best of Luck!

Answer:

-4, -1/7,0.09,π/2,√3 ,√225,17

Step-by-step explanation:

π/2, is approx 1.5

-4,

0.09,

17,

√3 is approx 1.7

,-1/7, is approx -.143

√225 = 15

From most negative to greatest

-4, -1/7,0.09,π/2,√3 ,√225,17

Answer:

[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]

Step-by-step explanation:

So we have the numbers:

[tex]\pi/2, -4, 0.09, 17, \sqrt3, -1/7, \sqrt{225}[/tex]

(And without using a calculator) approximate each of the values.

π is around 3.14, so π/2 is around 1.57.

17 squared is 289, so 1.7 squared is 2.89. Thus, the square root of 13 is somewhere between 1.7 and 1.8.

-1/7 can be divided to be about -0.1429...

And the square root of 225 is 15.

Now, use the approximations to place the numbers:

[tex]\pi/2\approx1.57; -4; 0.09;17;\sqrt3 \approx1.7; -1/7\approx-0.14;\sqrt{225}=15[/tex]

The smallest is -4.

Next is -1/7 or about -0.14

Followed by the first positive, 0.09.

And then with π/2 or 1.57

And then a bit bigger with the square root of 3 or 1.7.

And then with the square root of 225 or 15.

And finally the largest number 17.

Thus, the correct order is:

[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]

Answer:

Attachment 1 : Option A,

Attachment 2 : Option C

Step-by-step explanation:

( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.

6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals

( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...

The answer here will be option c, but let's prove it,

cos(5π / 3) = 1 / 2,

sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]

Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "

[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]

= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]

Hence proved that your solution is option c.

Answer:

18.90

Hope i got it right

Answer:

All real numbers.

Step-by-step explanation:

As there are no restrictions on the values of x, the domain is all real numbers.

Answer:

All real numbers.

Step-by-step explanation:

Complete Question

In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?

Answer:

The  probability is  [tex]P(g) =0.72[/tex]

Yes the result is reasonably close

Step-by-step explanation:

From the question we are told that

   The  number of  of  green peas is  [tex]g = 436[/tex]

     The number of yellow peas is  [tex]y = 171[/tex]

   The sample size is  [tex]n = 171 + 436 = 607[/tex]

The probability of getting an offspring pea that is green is mathematically represented as

       [tex]P(g) = \frac{g}{n}[/tex]

        [tex]P(g) = \frac{436}{607}[/tex]

        [tex]P(g) =0.72[/tex]

Comparing  [tex]P(g) =0.72[/tex]  to   [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close

Answer:

I think it  -1.50 to 10.58

Step-by-step explanation:

[tex]11x- xy +11y-x^2=\\-x^2-xy+11x+11y=\\-x(x+y)+11(x+y)=\\-(x-11)(x+y)[/tex]

Answer:

(x - 11)(-x - y)

Step-by-step explanation:

To factor the polynomial 11x - xy + 11y - x² completely, let's group the terms and factor them separately.

Rearranging the terms, we have:

11x - xy + 11y - x²

Let's rearrange the terms again to group similar terms together:

x² + 11x - xy + 11y

Now, we can factor out the common factor from each pair of terms:

x(-x + 11) - y(x - 11)

Simplifying further, we can factor out -1 from the first pair of terms:

-x(x - 11) - y(x - 11)

Now, notice that we have a common factor of (x - 11) in both terms. Factoring out this common factor, we obtain:

(x - 11)(-x - y)

Therefore, the polynomial 11x - xy + 11y - x² can be factored completely as (x - 11)(-x - y).

Answer:

DE

Step-by-step explanation:

I hope this helps!

Answer:

A. 14z - 28

Step-by-step explanation:

simplify z² - 3z

a. z(z - 3)

the denominator on the right has z(z - 3). but it is also multiplied by (z - 2)

this means the numerator must also be multiplied by (z - 2)

14 x (z - 2) = 14z - 28

hope this helps :)

Answer:

Time = 1.45152 seconds

Step-by-step explanation:

1 foot = 0.000189 mile

300 ft = 300*0.000189

300 ft = 0.0567 miles

492 ft = 492*0.000189

492 ft = 0.092988 miles

Distance left to be covered by the train

= 0.092988-0.0567

= 0.036288 miles

Speed= 90mph

Time taken = distance/speed

Time taken= 0.036288/90

Time = 4.032*10^-4 hour

Time = 4.032*10^-4*60*60

Time = 1.45152 seconds

Answer:

0.033316

Step-by-step explanation:

We use the z score formula to solve for this question.

Since we are given the number of samples in the question, our z score formula is given as:

z = (x-μ)/ S.E

where x is the raw score

μ is the sample mean

S.E is the Standard error.

x is the raw score = 900

μ is the sample mean = Population mean = 947

Standard error =

This is calculated as Population standard deviation/ √No of samples

= 205/√64.

= 205/8

= 25.625

We proceed to calculate the z score

z = (x-μ)/ S.E

z = 900 - 947/25.625

= -1.83415

Using the z score table for normal distribution,

P(x≤ z) = P(z ≤ -1.83) = P(x ≤ 900)

P(x<900) = 0.033316

Therefore, the probability the mean of the sample is below 900 is 0.033316

Answer:

Hi, sorry, please could you resend the question again this isn't clear enough to properly answer your question .

maybe you should type in the steps before it is answered. thanks

Answer:

answer= C

Step-by-step explanation:

Answer:

1078

Step-by-step explanation:

The product of 22 and 49 is 1078.

Answer:

1078 is the product

Step-by-step explanation:

Answer:

A service could be multiple things.

Step-by-step explanation:

Like, working as a scribe in a nursing home helping old people. Or, being part of a leadership club at school that funds food banks and things like that

Answer:

a

Step-by-step explanation:

Answer:

1 pound of Oranges = $2

1 pound of Bananas = $2

Step-by-step explanation:

O = Oranges

B = Bananas

=> 5o + 2b = 14

=> 2b = 14 - 5o

=> b = 14/2 - 5/2o

=> b = 7 - 2.5o

3o + 6b = 18

=> 3o + 6( 7 - 2.5o ) = 18

=> 3o + 42 - 15o = 18

=> -12o + 42 = 18

=> -12o = -24

=> -o = -2

=> o = 2

One pound of oranges costs $2.

So,

5 (2) + 2b = 14

=> 10 + 2b = 14

=> 2b =4

=> b = 2

One pound of bananas also costs $2.

Step-by-step explanation:

First we need to find out what they all 3 equal, with multiplication.

5×5=25

10×5=50

20×5=100

In each of these problems, the answer is multiplying itself by 2 in order to get to the next answer. So this is how they are related