A 16-ft ladder is placed 4 ft. from the base of a
building. How high on the building will the ladder
reach?

Answer:

9.434 X 10^66

Step-by-step explanation:

2.34 X 10^65  +  9.2 X 10^66    (First, you have to manipulate the exponents to bring them to the same index, i.e. the same power)

We can say that 2.34 X 10^65 = 0.234 X 10^66

Now that the indexes are equivalent, we can proceed to add the two bases together.

0.234 X 10^66  +  9.2 X 10^66

= (0.234  +  9.2) X 10^66

= 9.434 X 10^66

The sum of [tex]\(2.34 \times 10^{65}\)[/tex]and [tex]\(9.2 \times 10^{66}\)[/tex] is[tex]\(9.434 \times 10^{66}\)[/tex]

When adding numbers in scientific notation, it's crucial to align their exponents. In the case of[tex]\(2.34 \times 10^{65}\)[/tex] and [tex]\(9.2 \times 10^{66}\),[/tex] they don't initially share the same exponent. To rectify this, we need to adjust the first number.

First, express[tex]\(2.34 \times 10^{65}\)[/tex]as [tex]\(0.234 \times 10^{66}\)[/tex], moving the decimal point one place to the left. Now, both numbers are in the form[tex]\(A \times 10^{66}\),[/tex]making them compatible for addition.

Next, add the coefficients:[tex]\(0.234 + 9.2 = 9.434\).[/tex]

So, the result is[tex]\(9.434 \times 10^{66}\).[/tex] This number is significantly larger than either of the original numbers. In essence, we're combining a quantity in the tens (0.234) with one in the tens of billions (9.2), resulting in a massive number in the tens of billions of billions (9.434) times 10 raised to the power of 66.

In practical terms, this means that if you were to multiply[tex]\(2.34 \times 10^{65}\)[/tex]by 10 and then add[tex]\(9.2 \times 10^{66}\)[/tex]to it, you would have [tex]\(9.434 \times 10^{66}\)[/tex] as your final answer. This demonstrates the remarkable flexibility and ease of handling extremely large numbers using scientific notation.

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Answer: 6 (pi)

Step-by-step explanation:

Feta/3 = (arc)/Radius

The length of arc AB is approximately 18 centimeters.

The arc length ([tex]s[/tex]) of a circle section, in centimeters, is defined by the following formula:

[tex]s = \alpha \cdot r[/tex]   (1)

Where:

If we know that [tex]\alpha = \frac{\pi}{3}\,rad[/tex] and [tex]r = 18\,cm[/tex], then the length of the arc is:

[tex]s = \frac{\pi}{3}\cdot (18\,cm)[/tex]

[tex]s \approx 18.850\,cm[/tex]

The length of arc AB is approximately 18 centimeters. [tex]\blacksquare[/tex]  

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Answer:

7/12

Step-by-step explanation:

1/4 +1/3

We need to get a common denominator of 12

1/4*3/3 = 3/12

1/3 *4/4 = 4/12

3/12+4/12 = 7/12

Answer:

The answer is 7/12.

Explanation:

1/3 = 4/12

1/4 = 3/12

4 + 3 = 7

Answer:

Ans- A

Step-by-step explanation:

When you have a quadratic like this, f(x) = [tex]x^{2}[/tex] + x - 12,

factorize it first.

Then you'll get f(x)= (x-3)*(x+4)

Finally, you set:

0= (x-3)*(x+4)

Just use the null factor law, and there you go.

x= 3 or x=-4

Have a nice day :)

The zeros of the given quadratic equation is equivalent to 3 and -4. Option A

Given the quadratic equation below:

f(x) = x² + x - 12

Factorising the expression, we will have:

f(x) = x² + 4x - 3x - 12

Factor

f(x) = (x² + 4x) - (3x  + 12)

f(x) = x(x+4) - 3(x + 4)

f(x) = (x - 3)(x+4)

If f(x) = 0

(x - 3)(x+4) = 0

x = 3 and -4

Hence  the zeros of f(x) = x^2 + x - 12 are 3 and -4.

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Step-by-step explanation:

Given

x = -2

Now

y = 3x - 2

= 3 * (-2 )-2

= -6 - 2

= -8

Answer:

Scalene Triangle

Step-by-step explanation:

If you mark the points on the graph, all three sides have different lengths and angles, therefor it is a scalene triangle.

It cannot be a right triangke bc there is no right angle, and no obtuse either so that crosses out obtuse as an option as well. In order to be an isoceles triangle it must have two sides of equal length, but it does not.

Answer:

r=67.2

Step-by-step explanation:

Answer:

r = 67.2

Step-by-step explanation:

8.25r = 554.4

divide 8.25 from both sides

r = 554.4/8.25 = 67.2

r = 67.2

Answer:

The slope of the line on this graph is 1/2.

Step-by-step explanation:

From (-4, 0), go up 2 units to (-4, 2), then go right 4 units to (0, 2). So the slope of this line is 2/4 = 1/2.

Answer:

-8-2m

Step-by-step explanation:

Using distributive property

Hey there! :-)

The Distributive Property states the following:

a(b+c)=ab+ac

Where we distribute a by multiplying it times b and c

Now, let's simplify our expression:

-2(4+m)

-8-2m

or

-2m-8

Hence, the final answer is

[tex]\boxed{\boxed{\bold{-2m-8}}}[/tex]

Hope everything is clear.

Let me know if you have any other queries; if so, please comment.

#LearningDoesn'tEnd

P.S. Sorry for the late response!

Answer:

1/12 of the original

Step-by-step explanation:

If you split 1/4 into 3 equal pieces, then each friend gets 1/12 of the original cake

Answer:

Step-by-step explanation:

When solving algebra, it is important the we follow the steps in correct order and check our answer at the end.

Step 1: Simplify by combining like terms

y = -x/2 + 5/4 + 8y = -25

Step 2: Substitute

y = -25

-25 = -x/2 + 5/4 + 8(-25)

-25 = -x/2 + 5/4 + -200

-25 = -x/2 - 198 3/4

Step 3: Answer

x = -347 1/2

Step 4: Check

y = 3/2x + 5/4 −2x + 8y = −25

-25 = 3/2(-347 1/2) + 5/4 −2(-347 1/2) + 8(-25)

-25 = -25✔️

Step 5: Verified Answer

x = -347 1/2

I'm always happy to help :)

Answer:

wait is that rlly u?

Step-by-step explanation:

its me ethan

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The first unknown integer will be x. The second one will be y.

x^2 - xy = 100

This is the same one as

x^2 - xy - 100 = 0

Answer:

if barbecue chips don't have any votes then D is the answer, if they do have votes then the answer may be A

Step-by-step explanation:

Answer:

Its barbecue crisps because no one choosed it !

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

tell me if im wrong pls

Answer:

b

Step-by-step explanation:

Answer:

180 degrees

Step-by-step explanation:

It is a half circle

Answer:

The answer you should get is 9:3

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

I just did it and got it right.

Answer:

-38

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

he payed 8.10$

bobby wasted 14.4 on the red ribbon

bobby wasted 6134.4  on yellow ribbon

together he wasted 6148.8

Answer:

$ 8.1

Step-by-step explanation:

To find 4 1/2 ft of cable wire you need to find what one foot of cable wire is which is $1.80.

So now add $1.80 four times:

1.80 + 1.80 + 1.80 + 1.80 =  7.20

It will cost $7.20 for four feet of cable wire

Now you have to do a half of $ 1.80

1.8 / 2 = 0.90

Now add 7.2 and 0.90 together

7.2 + 0.9 = 8.10

So Peter would need to buy $ 8.10 of cable wire for 4 1/2 ft.

Answer:

8 acres of land they did not plant the corn.

Step-by-step explanation:

GIven:

There are 25 acres of land on a farm.

The owners planted corn on 68 percent of the land.

Now, to find the acres they did not plant the corn.

Total acres of land on the farm = 25 acres.

Rate of land owners planted the corn = 68%.

Now, to get the acres of land owners planted the corn:

[tex]68\%\ of\ 25\\\\=\frac{68}{100} \times 25\\\\=0.68\times 25\\\\=17\ acres.[/tex]

Thus, 3.4 acres of land owners planted the corn.

Now, to get the acres land owners did not planted the corn we subtract the acres of land owners planted the corn from the total acres of land:

[tex]25\ acres-17\ acres\\\\=8\ acres.[/tex]

Therefore, 8 acres of land they did not plant the corn.

Answer:

21

Step-by-step explanation:

5×3=15

7×3=21

Answer:

Step-by-step explanation:

a) The denominators of variable terms is 5 and 3

As both are prime, least common denominator = 5*3 = 15

b) The denominators of constant terms is 7 and 3

Least common denominator = 7*3 = 21

Answer:

141

Step-by-step explanation:

<1 and the angle measuring 39 degrees form a straight lines so they sum to 180 degrees.

<1 +39 = 180

Subtract 39 from each side

<1 +39-39 = 180-39

<1 = 141

Answer:

141 degrees

Step-by-step explanation:

Angle 1 is  on the straight line with 39 degree angle together would = 180

180 - 39 = 141 degrees

Answer:

50.24

Step-by-step explanation:

Take the diameter and multiply by 3.14 so 16 times 3.14

Answer:

State that the circunference of a circle is equal to:

[tex]C=\pi d[/tex], where C is the circumference and d is the diameter

So, once d = 16 in

Therefore, [tex]C=16\pi[/tex] in

Answer:

  11/10

Step-by-step explanation:

Your calculator will tell you that √58 ≈ 7.62 and √42 ≈ 6.48. The difference of these numbers is ...

  7.62 -6.48 = 1.14 ≈ 1.1

The difference is about 11 tenths.

_____

You should be able to count the divisions on the number line to arrive at this conclusion.

⇒ 1.2  is your answer.

System #1

2x + 3y = 12   and  4x + 3y = 18

I'd use elimination on this one; we subtract equations and the 3y disappears,

2x = 6

x = 3

3y = 18-4x = 18 - 4(3) = 18 = 12 = 6

y = 2

System #2

y = 2x +1  and  y =-3x -2

Here I'd use elimination; we have two things equal to y, we eliminate y by setting the right sides equal to each other,

2x + 1 = -3x - 2

5x = -3

x = -3/5

y = 2x+1 = -1/5

check y=-3x -2 = 9/5 - 10/5 = -1/5, good

System #3

x = 2y + 5  and x + 3y = 25

Here I'd use substitution.   The first equation is for x in terms of y; if we substitute it into the second equation we'll just have an equation in y.

(2y + 5) +3y = 25

5y + 5 =25

5y = 20

y = 4

x = 2y+5 = 13

Answer:

(a) There is 95% confidence that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

(b) The point estimate is 0.625. The margin of error is 0.15.

(c) It is plausible that the true proportion of all owners who greet their dog first is 66%.

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval. Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

In statistic, point estimation comprises of the use of sample data to estimate a distinct data value (known as a point estimate) which is to function as a "best guess" or "best estimate" of an unidentified population parameter. The point estimate of the population mean (µ) is the sample mean ([tex]\bar x[/tex]).

The  (1 - α)% confidence interval for population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The margin of error for this interval is:

[tex]MOE=\frac{UL-LL}{2}[/tex]

For the hypothesis test, if the confidence interval consist of the null value of the parameter then the null hypothesis is accepted or else rejected.

The 95% confidence interval for the population proportion of owners who greet their dog first is,

CI = (0.475, 0.775)

(a)

The 95% confidence interval for the population proportion, (0.475, 0.775), implies that there is a 0.95 probability that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

Or, there is 95% confidence that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

(b)

The point estimate of the population proportion (p) is the sample mean ([tex]\hat p[/tex]).

Compute the point estimate from the 95% confidence interval as follows:

Point estimate = (UL + LL)/2

                        [tex]=\frac{0.775+0.475}{2}\\=0.625[/tex]

The point estimate is 0.625.

Compute the margin of error as follows:

[tex]MOE=\frac{UL-LL}{2}=\frac{0.775-0.475}{2}=0.15[/tex]

The margin of error is 0.15.

(c)

The hypothesis to test whether the proportion of all owners who greet their dog first is 66% is:

H₀: The proportion of all owners who greet their dog first is 66%, i.e. p = 0.66

Hₐ: The proportion of all owners who greet their dog first is not 66%, i.e. p ≠ 0.66.

The 95% confidence interval for the population proportion of owners who greet their dog first is,

CI = (0.475, 0.775)

The 95% confidence interval consists of the null value, i.e. p = 0.66.

The null hypothesis was failed to rejected.

Thus, it is plausible that the true proportion of all owners who greet their dog first is 66%.

Answer:

Step-by-step explanation:

It's A. 90% confidence that between 42.5% and 47.9% of Americans own a dog

Answer:

Answers are below

Step-by-step explanation:

       3y = 10 - x

2x + 6y = 7                 This set is correct because it is lined up correctly.

      y =  13 - 2x

4x - y = -1                    This set is also correct because it is lined up correctly.

The equations that have no solutions are:

x + 4y = 23

   - 3x = 12y +1         These equations don't touch

       3y = 10 - x

2x + 6y = 7              These equations don't touch

If these answers are correct, please make me Brainliest!

Answer:

x + 4y = 23

- 3x = 12y +1

3y = 10 - x

2x + 6y = 7

Step-by-step explanation: