Write the numbers in scientific notation.
8. 5,100,000
9. .00000698
10. 3.000052
Write the numbers in standard form.
11. 6.548 x 10-3
12. 5.854 x 10' 58.54
13. 2.25 x 106​

Answer:

Step-by-step explanation:

Let's organise our information :

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

Now let's solve this equation :

Δ=1²-4*(1/2)*(-4)

 = 9

So we have two solutions :

So the solutions are -4 and 2

Answer:

53/28

Step-by-step explanation:

100 g jam

Blackberry / sugar= 53/28

Answer:

Solution,

Amount of sugar=100-(19+53)

=100-72

=28 gram

Ratio of blackberries to sugar=53/28

=53:28

Hope this helps..

Good luck on your assignment..

Answer: 20 cm

If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.

Given that

WX≅DC,

XY≅BC,

you can state that

YZ≅AB,

WZ≅AD.

If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.

The perimeter of WXYZ is

P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.

Answer:

1140 ways.

Step-by-step explanation:

The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).

The 17 identical candies, can be distributed among the 4 children in :  

=(17 + 4 - 1)C(4–1) = 20C3 ways.

= 20!/((20–3)!*3!) ways.

= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways

= 20*19*3 ways.  

=1140 ways.

Answer:

v = Δs/Δt

Step-by-step explanation:

Velocity is equal to the displacement/distance (delta symbol s) over the change of time (delta symbol t).

Answer:

1/9

Step-by-step explanation:

first, u need 9 ---> 1/3

then u need 8 ---> 1/3 also

Multiply them and get...1/9

Answer:

a) 294

b) 180

c) 75

d) 174

e) 105

Step-by-step explanation:

I assume that for each problem, the first digit can't be 0.

a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.

6×7×7 = 294

b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.

6×6×5 = 180

c) Again, each digit can only be used once, but this time, the last digit must be odd.

If only the last digit is odd, there are 3×3×3 = 27 possible numbers.

If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.

If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.

If all three digits are odd, there are 3×2×1 = 6 possible numbers.

The total is 27 + 24 + 18 + 6 = 75.

d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.

If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.

If the first digit is greater than 3, there are 3×7×7 = 147 numbers.

The total is 6 + 21 + 147 = 174.

e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.

If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.

The total is 15 + 90 = 105.

Answer:

36 cups

3/12 = 9/c

Step-by-step explanation

3 ÷ 12 = .25

each cup = 25 cents

9 ÷ .25 = 36

Marco sold 36 cups of lemonade.

3/12 = 9/c

Answer:

36 cups

Step-by-step explanation:

We can set up a proportion:

12/3=c/9

Cross multiply.

12*9=3*c

108=3c

Divide both sides by 3.

c=36

The error that the proportion Kaycee set up was

cups/price=price/cups

This is not proportionate.

Possible proportions include:

cups/price=cups/price

price/cups=price/cups

cups/cups=price/price

price/price=cups/cups

Answer:

here the order will be 104! =[tex]1.029e^{166}[/tex]

Step-by-step explanation:

since the cards are to arranged in  no particular order that is why we used combination to find the result.

Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.

Answer:

here,

a=b+12

b=a-12----> equation (i)

b= c+4

putting the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

hope this helps...

Good luck on your assignment...

The value of a + c is 16.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

a=b+12

So, b=a-12 ---- equation (i)

and, b= c+4

Substitute the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

Hence, the value of a+ c is 16.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ2

Answer:

P-value = 0.0367

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of residents who favor construction is significantly over 42%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.42\\\\H_a:\pi>0.42[/tex]

The sample has a size n=900.

The sample proportion is p=0.45.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.42*0.58}{900}}\\\\\\ \sigma_p=\sqrt{0.000271}=0.016[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.45-0.42-0.5/900}{0.016}=\dfrac{0.029}{0.016}=1.79[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.79)=0.0367[/tex]

Answer:

sum of the angles of the triangle are 180°

Step-by-step explanation:

To find the sum of the interior angles, we use the formula( s-2*180), where s is the number of sides of the shape. If it is a pentagon, 5-2*180= 3*180= 540,

which shows that the sum of the interior angles of a pentagon is 540.

since, it is a triangle in the figure with 3 sides, 3-2*180=1*180=180.

The interior angles are unknown= a, b and c. we know that a+b+c=180 degrees and the exterior angles are mentioned. And we know that, opposite angles are equal. So, a is 40 degrees considering that 40 degrees is the opposite angle of a, b is 95 degrees whereas c is 45 degrees.

now, lets check if the angles indeed have a sum of 180 degrees,

40+95+45= 135+45 which gives 180 degrees.

Answer:

180°

Step-by-step explanation:

→ Angles in a triangles always add up to 180, we can prove this by calculating a, b and c so,

a = 40° (vertical angles are equal)

b = 95° (vertical angles are equal)

c = 45° (vertical angles are equal)

40 + 45 + 95 = 85 + 95 = 180°

Answer:

Test statistic t = 3.12

P-value = 0.001

As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year (Gina's claim).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=55000\\\\H_a:\mu> 55000[/tex]

The significance level is 0.05.

The sample has a size n=61.

The sample mean is M=56500.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3750.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3750}{\sqrt{61}}=480.138[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{56500-55000}{480.138}=\dfrac{1500}{480.138}=3.12[/tex]

The degrees of freedom for this sample size are:

df=n-1=61-1=60

This test is a right-tailed test, with 60 degrees of freedom and t=3.12, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>3.12)=0.001[/tex]

As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.

Answer:

1. The 99% confidence interval is from 941.527 to 958.473

2. The 99% confidence interval is from 933.054 to 966.946

3. The 99% confidence interval is from 916.108 to 983.892

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sample size,

s is the sample standard deviation,

[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level

The t-score corresponding to 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 13 - 1 = 12

From the t-table at α = 0.005 and DoF = 12

t-score = 3.055

1. 99% Confidence Interval when s = 10

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]

The 99% confidence interval is from 941.527 to 958.473

2. 99% Confidence Interval when s = 20

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]

The 99% confidence interval is from 933.054 to 966.946

3. 99% Confidence Interval when s = 40

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]

The 99% confidence interval is from 916.108 to 983.892

As the sample standard deviation increases, the range of confidence interval also increases.

Answer:

3: 2

Step-by-step explanation:

game Apps: education apps:

3: 2

Answer: graphing calculator!

Step-by-step explanation: if you’re looking for the square root of a # that isn’t a perfect square (ie. sqrt4, sqrt 36) then you have to use a calculator for that. however the idea behind square roots is just a # multiplied by itself to give the original #. just ask yourself “what can i multiply by itself to get the original number”. hope that helped !

Answer:

By multiplying the number by its power 2.

E.g= 4^2

Answer:

2

Step-by-step explanation:

I would have to say it is two bc Everitt had 30% where Desery had 20%.

Answer:

Hope it helps you :)

And i hope you understand  

For store 1, it can be placed on 16 sites. Store 2 can be placed on 15 sites( since store 1 is already on site 1). Store 3 can be placed on 14 sites and so on until store 5 which has 12 sites.

Therefore the number of way is

C= 16*15*14*13*12

c=524,160 possibilities

Answer:

Option B

Step-by-step explanation:

Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -

[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]

Convert this to slope - intercept form -

[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]

Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -

( 0, 10 ),

( 15, 9 ),

( 17, 0 )

When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -

Option B

Answer:

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X¿ 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s¿4.2 represent the sample standard deviation

n¿65 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]    

Answer:

She is saving 10 cents per pound

Step-by-step explanation:

First, we need to find how much she would pay without the sale:

12.5(1.8) = 22.5

Now, we can calculate how much she saved:

22.5 - 21.25 = 1.25

To find how much she's saving per pound, we divide the difference by the number of pounds:

1.25/12.5 = 0.1

She is saving 10 cents per pound

Answer:

A

Step-by-step explanation:

I took the test and got it right

Answer:

29.4

Step-by-step explanation:

Answer:

2.94

Step-by-step explanation:

4.2 × 0.7 = 2.94

Answer:

The answer is 1/27

Step-by-step explanation:

According to the rules of indices

a^-b can be written as 1/a^b

So 3^- 3 can be written as 1/3³

And

1/3³ = 1/27

Hope this helps you

Answer:

3c - 7

Step-by-step explanation:

c - the number of miles Lawrence biked

Tammy biked seven less than three times the number of miles that Lawrence biked.

So, 3 x c (the # of miles Lawrence biked) - 7 (she biked seven less)

The answer is 3c - 7.

Answer:

5

Step-by-step explanation:

(14 × 5 × 4) ÷ (28 × 2)

Solve brackets.

280 ÷ 56

Divide.

= 5

Answer:

A)x=2pi/3 and x=-2pi/3

Step-by-step explanation:

The function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values where the tan(a) has vertical asymptotes.

we know that tan(a) has vertical asymptotes in [tex]a=\frac{\pi }{2}[/tex] and  [tex]a=\frac{-\pi }{2}[/tex], if we made [tex]a=\frac{3x}{4}[/tex] and solve for x, we get:

for [tex]a=\frac{\pi }{2}[/tex]

[tex]\frac{\pi }{2} =\frac{3x}{4}\\x = \frac{2\pi }{3}[/tex]

for [tex]a=\frac{-\pi }{2}[/tex]

[tex]\frac{-\pi }{2} =\frac{3x}{4}\\x = \frac{-2\pi }{3}[/tex]

Finally, the function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values x=2pi/3 and x=-2pi/3

Answer:

A

Step-by-step explanation:

Answer:

The time period is 13 years.

Step-by-step explanation:

Interest rate (r )= 5% or 5%/12 = 0.42% per months

The investment amount (Present value) = $10500

Final expected amount (future value) = $20000

Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.

Use the below formula to find the time period.

Future value = present value (1 + r )^n

20000 = 10500(1+0.0042)^n

1.9047619 = (1+0.0042)^n

1.9047619 = 1.0042^n

n = 153.74 months.

Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)

Answer:

m∠s = 93°

Step-by-step explanation:

We know that any quadrilateral's sum of angles adds up to 360°. In that case,

360 - (56 + 132 + 79) = m∠s

m∠s = 93°

Answer:

S° = 93 °

Step-by-step explanation:

[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]

Answer:

fg t f h 10

Step-by-step explanation:

Hey there! :)

Answer:

56 m².

Step-by-step explanation:

To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:

Solve for the rectangle: (A = l × w)

A = 8 × 5

A = 40 m²

Solve for the triangle: (A = 1/2 (bh))

A = 1/2(4 · 8)

A = 1/2(32)

A = 16 m².

Add up the two areas:

40 + 16 = 56 m².

Answer:

Area of triangle+ the area of rectangle

Step-by-step explanation:

Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²

Area of rectangle is length × breadth= 5×8: 40 m²

Area of the shape is 40m²+16m²= 56m²