Evaluate the expression
[3(15+4)2 +2(20+5)2]0
0
5
1
2

Answer:

See image

Step-by-step explanation:

This is to help you practice exponent rules. The rules are short cuts, which are good bc they're faster but bad bc they take away the meaning of the work. If you're trying to remember a rule, think through the meaning. See image.

So, "multiply exponents" and "product of powers" are basic two equivalent phrases! I think the answers on the image should work, but jic if not switch those two.

The Add exponents rule and Subtract are 100% correct.

The expressions are matched to the method needed to evaluate as shown below.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The first expression is 5³ × 5³.

Multiplication rule of exponents states that,

xᵃ × xᵇ = xᵃ⁺ᵇ

That is we add the exponents.

So, 5³ × 5³ = 5³⁺³ = 5⁶

The next expression is (7²)³.

We have the rule, (xᵃ)ᵇ = xᵃᵇ

So, here, multiply the exponents.

(7²)³ = 7⁶

(4x³)⁵

We can write it as,

(4x³)⁵ = 4⁵ . (x³)⁵

That is write is as product of the powers.

Division rule of exponents states that,

xᵃ / xᵇ = xᵃ⁻ᵇ

6⁹ / 6⁵ = 6⁹⁻⁵ = 6⁴

So, subtract the exponents.

Hence the expressions are matched.

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Answer:

[tex]a=\frac{7}{3}[/tex]

Step-by-step explanation:

[tex]\frac{a-1}{a-3}=\frac{a+1}{a-4}[/tex]

[tex](a-1)(a-4)=(a-3)(a+1)[/tex]

[tex]a^2-5a+4=a^2-2a-3[/tex]

[tex]-5a+4=-2a-3[/tex]

[tex]-3a+4=-3[/tex]

[tex]-3a=-7[/tex]

[tex]a=\frac{7}{3}[/tex]

Answer:

Step-by-step explanation:

Jeremy

Pay = 800

Time = 40 hours

Per hour pay= 800/40 = 20 dollars per hour.

Beth

Pay = 700

Time = 30 hours

Per hour Pay= 700 / 30 = 23.33

The answer is C. She gets 23.33 which is 3.33 more than her brother makes.

Answer:

Slope (known as m) = -3/2; Y-int (known as b) = 3

Step-by-step explanation:

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{{0}-{3}}{{2}-{0}}[/tex]

m = [tex]\frac{-3}{2}[/tex]

b = [tex]3[/tex]

Answer:

Step-by-step explanation:

A + B = 90

A/6(15.25) = 3B/4

61A/18 = B

18A/18 + 61A/18 = 90

A = 90(18)/79

A = 20 40/79°

B = 90 -A = 69 39/79°

Answer:13 percent would have cats and the other 13 percent wouldn’t

Step-by-step explanation:plz mark for brainlist

Thank you

Answer: the answer is x=72

Step-by-step explanation:

Step 1: simplify both sides we know 15=x/4 -3 (the x holds a invisible 1)

the equation should look something Like: 15=1/4x-3 then FLIP the equation such as:

1/4x-3=15 then add 3 on both sides so 15+3=18

step 2: our equation is now 1/4x=18  (we see 4 is being divided the opposite of division is multiply) therefor multiply the 18 with 4

18*4=72 which means x=72

Answer:

y= 2x +1

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the gradient and c is the slope.

Since all the slope in the options are the same, let's focus on the y-intercept. From the graph, the line cuts through the y-axis at y= 1. Thus, the y- intercept is 1.

Hence, y= 2x +1 is the correct option.

Extra notes:

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Answer:

Y Intercept: 0, 2.5

X Intercept: 3.5, 0

Explanation:

An Intercept is where a line crosses an axis. A Y Intercept is for the Y axis and the X intercept is for the X axis.

Also when writing coordinates, the x coordinate comes before the y one.

Hope this helps :)

Answer:

7,200 words

Step-by-step explanation:

Answer: 4,800

I multiplied 120 by 20 because 60 divided by 3 is 20. Then I multiplied my answer by 2 because the question is asking how many words could they type in 2 hours

Answer:

A' = (-4, 7)

B' = (3, 5)

C' = (1, 2)

Step-by-step explanation:

The question is asking you to translate the function by adding 4 to the x-value of each point and 2 to the y-value of each point.

I didn't double-check my math, but since the question is asking for an ordered pair, this should be correct.

Answer:

between 1hr 30 and 1hr 45

Step-by-step explanation:

10*2=20                                 15

20*2=40                                 30

40*2=80                                 45

80*2=160                                 60

160*2=320                                 1hr 15

320*2=640                                 1hr 30

In 90 minutes the population to grow to 700 organisms.

Given that,

A strand of bacteria has a doubling time of 15 minutes.

If the population starts with 10 organisms.

We have to determine,

How long would it take for the population to grow to 700 organisms?

According to the question,

A strand of bacteria has a doubling time of 15 minutes.

If the population starts with 10 organisms.

In 15 minutes strand of bacteria has a doubling time the population starts with 10 organisms.

[tex]\rm = 10 \times 2 = 20 \ bacteria[/tex]

In 15 minutes 20 bacteria for the population to grow.

In 30 minutes strand of bacteria has a doubling time the population starts with 20 organisms.

[tex]\rm = 20 \times 2 = 40 \ bacteria[/tex]

In 30 minutes 40 bacteria for the population to grow.

In 45 minutes strand of bacteria has a doubling time the population starts with 40 organisms.

[tex]\rm = 40 \times 2 = 80 \ bacteria[/tex]

In 45 minutes 80 bacteria for the population to grow.

In 60 minutes strand of bacteria has a doubling time the population starts with 80 organisms.

[tex]\rm = 80 \times 2 = 160 \ bacteria[/tex]

In 60 minutes 160 bacteria for the population to grow.

In 75 minutes strand of bacteria has a doubling time the population starts with 160 organisms.

[tex]\rm = 160 \times 2 = 320 \ bacteria[/tex]

In 75 minutes 320 bacteria for the population to grow.

In 90 minutes strand of bacteria has a doubling time the population starts with 320 organisms.

[tex]\rm = 320 \times 2 = 640 \ bacteria[/tex]

In 90 minutes 640 bacteria for the population to grow.

In 120 minutes strand of bacteria has a doubling time the population starts with 640 organisms.

[tex]\rm = 640 \times 2 = 1280 \ bacteria[/tex]

In 120 minutes 1280 bacteria for the population to grow.

Hence, In 90 minutes the population to grow to 700 organisms.

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Answer:

Step-by-step explanation:

The second equation is y = -5x - 19

The first equation needs a little work

y - 9 = -5(x + 2)                                         Remove the brackets

y - 9 = -5x - 10                                          Add 9 to both sides.

y = -5x -10 + 9                                          Combine

y = - 5x - 1

There are two lines there. They are parallel, but they never cross. The y intercepts are not equal and they don't lie on top of each other.

Answer:

Step-by-step explanation:

The slope- intercept form is:

We have:

The line is:

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

[tex]P(X = r) = nCr * p^{r} * (1 - p)^{n - r}[/tex]

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \impliedby y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x+7 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{5}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}[/tex]

so then line K has a slope of -5 and pass through (-1, -3)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad \qquad slope=m=-5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-5}[x-\stackrel{x_1}{(-1)}] \\\\\\ y+3=-5(x+1)\implies y+3=-5x-5\implies y=-5x-8[/tex]

Answer:

Step-by-step explanation:

The problem statement is not clear regarding which money is invested. We will assume it is the 80% of $8750 that is set aside for future education. That amount is

... 0.80 × $8750 = $7000

If x represents the amount invested at 7%, then the total interest earned is

... (7000 -x)×4% + (x)×7% = 420

... 280 +0.03x = 420

... x = 140/0.03 ≈ 4666.67

$4666.67 was invested at 7%.

$2333.33 was invested at 4%.

[tex]-2(x+1) = -2+5\\\\\implies -2x -2 = 3\\\\\implies -2x = 3 +2 =5\\\\\implies x = - \dfrac 52[/tex]

Add the numbers, then add 2 to both sides of the equation. The solution would be x = - 5/2

Answer:

2nd answer choice

Step-by-step explanation:

We want to know which one does not have a two digit quotient, or answer. Let us use guess and check since there are only 4 options.

Option 1:

519/6=86 R3

This answer is wrong because it has a two digit quotient

Option 2:

915/7=130 R5

This answer is correct since it has a three digit quotient, but let's find the rest

Option 3:

439/7=62 R5

This answer is wrong because it has a two digit quotient

Option 4:

812/9=90 R2

This answer is wrong because it has a two digit quotient

Therefore option 2 is correct

I will like to know what you need help with?

Answer:

X-intercept at (1/2 ,0)

domain of (0, infinity)

Vertical asymptote of x = 0

Step-by-step explanation:

Plato I got it right on the test

Answer:

class C

Step-by-step explanation:

a=(17/25)=0.68

b=(13/20)=0.65

c=(7/10)=0.7

Answer:

the portion of the drama clubs budget needed for each type of expense

Step-by-step explanation:

the number of inches of snow received each year by a ski resort

- you should use line graph to see data changing in consistent time period

the portion of the drama clubs budget needed for each type of expense

- you can use box plot to see the box plot to show median and q1 q3 of the expenses.

the number of heads and tails that came up in 100 coin flips

- you should use pie chart to see the percentages in entire population  

the number of votes received by each of four candidates

- you should use bar graph to compare 4 comparable object.

The portion of the drama clubs budget needed for each type of expense

A data set is a set of information. A data set corresponds to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row represents a specific record of the data set in question.

a) The number of inches of snow received each year by a ski resort

you should use a line graph to see data changing in the consistent time period

b) The portion of the drama club budget needed for each type of expense

you can use the box plot to see the box plot to show the median and q1 q3 of the expenses.

c) The number of heads and tails that came up in 100 coin flips

you should use a pie chart to see the percentages in the entire population  

d) The number of votes received by each of the four candidates

you should use a bar graph to compare 4 comparable objects.

Therefore a portion of the drama club's budget is needed for each type of expense.

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Answer:

207+ 364 = 571

Step-by-step explanation:

i guess?._.