Find the value of x and y in the parallelogram below.

Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question:

[tex]t = 35, I = 0.07, T = 1700000[/tex]

She has to invest P today.

[tex]T = E + P[/tex]

[tex]1700000 = E + P[/tex]

[tex]E = 1700000 - P[/tex]

So

[tex]E = P*I*t[/tex]

[tex]1700000 - P = P*0.07*34[/tex]

[tex]3.38P = 1700000[/tex]

[tex]P = \frac{1700000}{3.38}[/tex]

[tex]P = 502958.58[/tex]

Sarah has to invest $502,958.58 today.

Answer:

The low tide, when it is 10 feet below the high tide would be at 7am and 7pm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;

[tex]\overline x = \frac{\sum fx}{\sum f} \\[/tex]

[tex]\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F[/tex]

The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)

Answer:

55.56  or  55 5/9

Step-by-step explanation:

To find the time it takes to type a report, you need to divide the number of words in the report by the words the typist can type in a minute.

2500/45 = 55.56

It takes 55.56 minutes or 55 5/9 minutes to type a 2500 word report.

Answer:

55 minutes and 33 seconds.

Step-by-step explanation:

To solve this we can set up a proportion.

1/45=x/2500

Cross multiply.

1*2500=45*x

45x=2500

Divide both sides by 45.

x=55.5*

.5* minutes is about 33 seconds. (0.55555*60)

So, it will take him around 55 minutes and 33 seconds.

Answer:

63 miles       x miles

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

3 gallons    7 gallons

Step-by-step explanation:

We will use proportions.  the number of miles over the gallons of gas

63 miles       x miles

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

3 gallons    7 gallons

Answer: 147 miles

Step-by-step explanation:

On 3 gallons, he travelled 63 miles

On 7 gallons, he travels

7/3 x 63 = 147 miles

Answer:

Null hypothesis: the variance in hours of usage for talking is not greater than the the variance in hours of usage for internet.

[tex]H_o[/tex]: [tex]\sigma _1 ^2 \leq \sigma _2^2[/tex]

Alternative hypothesis: the variance  in hours of usage for talking is  greater than the the variance in hours of usage for internet.

[tex]H_a : \sigma_1^2 > \sigma_2^2[/tex]

[tex]\mathbf{s_ 1 =16.11}[/tex]

[tex]\mathbf{s_2 = 7.98}[/tex]

Step-by-step explanation:

Let [tex]x_1[/tex] and [tex]x_2[/tex] be the two variables that represents the battery life in hours for talking usage and battery life in hours for internet usage respectively.

The hypothesis can be formulated as:

Null hypothesis: the variance in hours of usage for talking is not greater than the the variance in hours of usage for internet.

[tex]H_o[/tex]: [tex]\sigma _1 ^2 \leq \sigma _2^2[/tex]

Alternative hypothesis: the variance  in hours of usage for talking is  greater than the the variance in hours of usage for internet.

[tex]H_a : \sigma_1^2 > \sigma_2^2[/tex]

The standard deviation for the battery usage for talking is :

[tex]\bar x_1 = \dfrac{1}{n_1} \sum x_i \\ \\ \bar x_1 = \dfrac{1}{12}(35.8 +22.4+...+35.5) \\ \\ \bar x_1 = \dfrac{241.2}{12} \\ \\ \bar x_1 =20.1[/tex]

The standard deviation Is:

[tex]s_ 1 = \sqrt{\dfrac{1}{n_1-1}\sum (x{_1i}-\bar x_i)^2}[/tex]

[tex]s_ 1 = \sqrt{\dfrac{1}{12-1}\sum (35.8- 20.1)^2+ (35.5-20.1)^2}[/tex]

[tex]s_ 1 = \sqrt{259.568}[/tex]

[tex]\mathbf{s_ 1 =16.11}[/tex]

The standard deviation for the battery life usage for the internet is :

[tex]\bar x_2 = \dfrac{1}{n_2} \sum x_{2i}[/tex]

[tex]\bar x_2 = \dfrac{1}{10} (24.0+12.5+36.4+...+4.7})[/tex]

[tex]\bar x_2 = \dfrac{115}{10}[/tex]

[tex]\bar x_2 = 11.5[/tex]

Thus; the standard deviation is:

[tex]s_2 = \sqrt{\dfrac{1}{n_2-1}(x_{2i}- \bar x_2)^2}[/tex]

[tex]s_2 = \sqrt{\dfrac{1}{10-1}(24-11.5)^2+(4.7-11.5)^2}[/tex]

[tex]s_2 = \sqrt{63.60}[/tex]

[tex]\mathbf{s_2 = 7.98}[/tex]

Answer:

2.5 pounds

Step-by-step explanation:

Answer:

0.9 grams

Step-by-step explanation:

The point estimate for the average weight of Soap Bar A is:

[tex]A=\frac{121+122+124+ 123+ 120+ 124+ 121+ 121+ 121+ 123+ 120}{11}\\A=121.82\ grams[/tex]

The point estimate for the average weight of Soap Bar B is:

[tex]B=\frac{121+120+122+ 119+ 121+ 122+ 122+ 120+ 120 +121+ 122+123+119}{13}\\B=120.92\ grams[/tex]

Therefore, the point estimate for the true difference between the given population means is:

[tex]Dif = A-B\\Dif = 121.82-120.92\\Dif=0.9\ grams[/tex]

The point estimate for the difference is 0.9 grams.

Answer:

two to the thrid power is 8.

Step-by-step explanation:

2^3= 8

Answer:

I'm not sure what exactly the question is but it should be 8

Step-by-step explanation:

2^3

2×2×2=8

Answer:

(0,0)

Step-by-step explanation:

If a point satisfies both functions, they must be equal to each other. Thus, we have:

[tex]f(x)=g(x)[/tex]

[tex]2x=3x[/tex]  

The only x that satisfies this is 0.

Therefore, the y is also zero.

The point is (0,0).

Alternatively, you can also visualize the graphs. The only point where the graphs will touch is the origin point or (0,0).

Answer:

m>n

Step-by-step explanation:

The value of m

The sum of the angles of a triangle are 180

50+30 + m = 180

m = 180-50-30

m = 100

The value of n

The sum of the angles of a triangle are 180

28 + 58+n = 180

n = 180-58-28

n=94

m>n

Answer:

  A = 51.3°, B = 90°, C = 38.7°

Step-by-step explanation:

The given lengths satisfy the Pythagorean theorem:

  (√41)² = 4² +5²   ⇒   41 = 16 +25

so we know the triangle is a right triangle. The right angle is opposite the longest side, so is angle B, opposite side AC.

The remaining angles can be found using trig functions. For example, we know ...

  tan(A) = BC/AB = 5/4

  A = arctan(5/4) ≈ 51.3°

Then the other acute angle is ...

  C = 90° -51.3° = 38.7°

Angles A, B, C are ...

  (A, B, C) = (51.3°, 90°, 38.7°)

Answer:

c = ± 8.363277

Step-by-step explanation :

[tex]5.72^{2} = 32.49\\\\6.12^{2} = 37.4544\\3.49 + 37.4544 = 69.9444\\\\c^{2} = \sqrt{69.9444} \\= 8.363277[/tex]

Answer:

a) Null hypothesis: [tex] \mu \geq 863[/tex]

Alternative hypothesis: [tex] \mu >863[/tex]

b) For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

[tex] z_{\alpha}=-1.64[/tex]

And the rejection zone would be:

[tex] z<-1.64[/tex]

c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

d) [tex] p_v = P(z<-2.17) =0.015[/tex]

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Step-by-step explanation:

Part a

We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:

Null hypothesis: [tex] \mu \geq 863[/tex]

Alternative hypothesis: [tex] \mu >863[/tex]

Part b

For this case using the significance level of [tex]\alpha=0.05[/tex] we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

[tex] z_{\alpha}=-1.64[/tex]

And the rejection zone would be:

[tex] z<-1.64[/tex]

Part c

For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

Part d

For this case the p value would be given by:

[tex] p_v = P(z<-2.17) =0.015[/tex]

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Answer:

16 and 21/44  or 725/44

Step-by-step explanation:

convert 6 and 1/4 into an improper fraction; 25/4

convert 2 and 7/11 into an improper fraction; 29/11

multiply them together. [tex]\frac{25}{4}[/tex] × [tex]\frac{29}{11}[/tex]

you can do 25 × 29 to get  725

you can also do 4 × 11 to get 44.

725/44 simplifies to 16 and 21/44.

Answer:

[225(pi)]/4

Step-by-step explanation:

circumference = pi(diameter)

area = pi (radius)^2

Diameter = 2(radius)

15pi cm = pi(diameter)

divide both sides by pi

diameter = 15

radius = 7.5

Area = pi (7.5)^2

A  = 56.25 pi

most teachers prefer fractions so

225pi/4

Answer:

Step-by-step explanation:

Here we have,

E(X) = 1, var(X) = 3, E(Y) = 0, var(Y) = 4

Since X and Y has normal distribution so W will also have normal distribution with mean

E(W) = E(05X-Y+6)

= 0.5E(X) - E(Y) +6

= 0.5* 1 -0+ 6

= 6.5

and variance

Var(W) = Var(0.5X-Y+6)

= 0.25Var(X)+Var(Y)

= 0.25 * 3 + 4

= 4.75

(b)

The z-score for W = 6 is

[tex]z=\frac{6-6.5}{\sqrt{4.75} } \\\\=-0.23[/tex]

The required probability is:

P(W>6) = P(z > -0.23)

= 0.5910

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

Tangents that meet at a point are equal in length so DB = CB

Let's form an equation:

10x + 16 = 5x + 20

- 16 from both sides

10x = 5x + 4

- 5x from both sides

5x = 4

/5 on both sides

x = 4/5

Sub this value into the expression for CB

5(4/5) + 20 = 24

Thus, the answer is option D. 24

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Answer:

4TH OPTION

Step-by-step explanation:

IN A CIRCLE , TANGENT DRAWN FROM AN EXTERNAL POINT TO THE CIRCLE ARE EQUAL.

ie BD = BC

ie 10x +16 = 5x+20

10x - 5x = 20 -16

5x = 4

x = 4/5

therfore BC = 5x+20 = 5*4/5 +20

BC= 4+20

BC = 24

HOPE IT HELPS...

Answer:

The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.

Step-by-step explanation:

We can correct the values of the mean and standard deviation using the properties of the mean and the variance.

To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:

[tex]Y=1.3(X+0.2)[/tex]

The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.

Then, we can apply the properties of the mean as:

[tex]E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63[/tex]

For the standard deviation, we apply the properties of variance:

[tex]V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025[/tex]

The properties that have been applied are:

[tex]1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0[/tex]

Answer:

2.555555

Step-by-step explanation: Nine times 2 is 18. When we subtract 18 from 23 we get 5. In the quotient we add a decimal point and add a zero to 5 which is 50. Nine times 5 is 45. When we subtract 45 from 50 we get 5 again and again and again . In decimal form it is 2.5555555.

Answer:

2.55 Hope this helps!

Answer:

The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.

Step-by-step explanation:

When you graph this equation, you should see the zeros it passes and touches.

Answer:

A. The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.

Step-by-step explanation:

Answer:

  D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3)

Step-by-step explanation:

Adding (-1, 2) to each of the coordinates gives ...

  D +(-1, 2) = (-1-1, 3+2) = D'(-2, 5)

  E +(-1, 2) = (4-1, 3+2) = E'(3, 5)

  F +(-1, 2) = (4-1, 1+2) = F'(3, 3)

  G +(-1, 2) = (-1-1, 1+2) = G'(-2, 3)

Answer:

The answer is B.

Step-by-step explanation:

I got it correct on Edge 2020

Answer:

ED = 26

Step-by-step explanation:

Using tangent-secant theorem

(12)²=(8)(x+10)

144=8x+80

144-80=8x

8x = 64

x=8

Now

ED = 8+8+10

ED = 26

Answer:

26

Step-by-step explanation:

Applying the tangent-secant theorem, we get:

12^2 = 8 * (x + 10)

144 = 8x + 80

= 8x = 144 - 80

8x = 64

x = 8

Putting x = 8 in ED, which is x + x + 10, we get:

= 8 + 8 + 10

= 26

Hope this helps!

Answer:

​P(not less than 5) = 0.5

Step-by-step explanation:

Given

Parts of spinner = 8 equal parts

Required

​P(not less than 5)

First, it'll be assumed that the parts of the spinner is numbered 1 - 8.

This gives the following sample space (S)

S = {1,2,3,4,5,6,7,8}

Total = 8

To calculate PP(not less than 5), the number of parts not less than 5 is needed.

Parts not less than 5 = {5,6,7,8}

Number of parts = 4

So, ​P(not less than 5) = Number of parts not less than 5 divided by total number of parts

Mathematically, P(not less than 5) = 4/8

​P(not less than 5) = 4/8

​P(not less than 5) = ½

​P(not less than 5) = 0.5

Hence, the theoretical probability of PP(not less than 5) is 0.5.

Answer:

64√2 or 64 StartRoot 2 EndRoot

Step-by-step explanation:

A 45-45-90 traingle is a special traingle.  Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem.  Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2.  2(x)^2=c^2.  You then square root both sides and get c= x√2.  

Therefore, the two legs are x and the hypotenuse is x√2.  x√2=128 because the question says that the hypotenuse is 128.  Solve for x by dividing both sides by √2.  X=128/√2.  You rationalize it by multiplying the numberator and denominator of the fraction by √2.  √2*√2= 2.

X=(128√2)/2= 64√2 cm.

Since X is the leg, the answer would be 64√2

Answer:

B.

Step-by-step explanation:

Answer:

Total chocolates= 48

Each friend get 3 chocolates

Step-by-step explanation:

Ray has 3 boxes of chocolates = 3

Each box has 4 layers of chocolates

= 4

Each layer has 4 rows of 4 chocolates each= 4

Total number of chocolates = 3*4*4

Total number of chocolates

= 48 chocolates

He shares 48 chocolates among 16 friends.

They Will all obtain 48/16= 3 chocolates each

Answer: the correct answer is 12

Answer:

  7.07

Step-by-step explanation:

The area of the whole circle is given by the formula ...

  A = πr^2

For the given values, the area of the circle is ...

  A = 3.14(3 in)^2 = 28.26 in^2

One-quarter of that area is ...

  (28.26 in^2)/4 = 7.065 in^2

The area of the quarter-circle is about 7.07 square inches.

Answer:

[tex] = 7.065 {in}^{2} [/tex]

Step-by-step explanation:

[tex] area = \frac{90}{360} \times \pi {r}^{2} \\ \frac{1}{4} \times 3.14 \times 3 \times 3 \\ = \frac{28.26}{4} \\ = 7.065 \: \: {in}^{2} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

84

Step-by-step explanation:

Basically the ratio was multiplied by 12 to get the number of boys so you do the same to the other one.

Answer:

number of boys+number of girls=48boys+36girls=84members

Step-by-step explanation:

FIRST WE FIND THE NUMBER OF GIRLS BY STATISTICAL METHOD

4:3=48:x

4/3=48/x

By cross multiplication

4×x=48×3

4x=144

Dividing 4 on both sides

4x/4=144/4

x=36=number of girls

Answer:

[tex] P(X=3)[/tex]

And using the probability mass function we got:

[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]

Step-by-step explanation:

Let X the random variable of interest "number of times that 6 appears", on this case we now that:

[tex]X \sim Binom(n=12, p=1/6)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X=3)[/tex]

And using the probability mass function we got:

[tex] P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974[/tex]

Answer:

The answer is x ≤ 2.

Step-by-step explanation:

Firstly, you have to move the unrelated term to the other side :

[tex] - 9 \leqslant 7 - 8x[/tex]

[tex] - 9 - 7 \leqslant - 8x[/tex]

[tex] - 16 \leqslant - 8x[/tex]

Next you can solve it :

[tex] - 8x \geqslant - 16[/tex]

[tex]x \leqslant - 16 \div - 8[/tex]

[tex]x \leqslant 2[/tex]

*Remember to change the symbol, when it is dividing by a negative value