The area of the isosceles triangle is 80 square centimeters. Use the equation 1/2(8h) =80 to find the height of the triangle.

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Step-by-step explanation:

I hope this helps! Have a good rest of your day:)

The response of an LTI system to each signal should be simple enough in structure to provide us with a convenient representation of the response of the system to any signal constructed.

as a linear combination of the basic signal, Both of these properties are provided by Fourier analysis, The importance of complex exponentials in the study of the LTI system is that the response of an LTI system to a complex exponential input is the same complex exponential with only a change.

in amplitude; that is Continuous time: st e ® H(s)e, (3.1) Discrete-time: n n z ® H(z)z, (3.2) here the complex amplitude factor H(s) or H(z) will be in general be a function of the complex variable s or z, A signal for which the system output is a (possibly complex) constant times the input is referred.

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Answer:

(-6,6)

Step-by-step explanation:

Answer:

Step-by-step explanation:

17

Answer:

$30 , (0,30) is the y-int

Step-by-step explanation:

hope this helps!    :)

Answer:

24 inches

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(18^{2}\) + \(b^{2}\) = \(30^{2}\)

324 + \(b^{2}\) = 900

\(b^{2}\) = 576

\(\sqrt{b^{2} }\) = \(\sqrt{576}\)

b  = 24

Answer:

24 inches

Step-by-step explanation:

Since the size of the screen is measured from the lower corner to the opposite upper corner.

therefore it forms a right angled triangle.

given hypotenuse is 30inch

the height is 18 inches

using the Pythagorean theorem

\( {hypotense}^{2} = {width}^{2} + {height}^{2} \)

then

\( {30}^{2} = {width}^{2} + {18}^{2} \\ 900 = {width}^{2} +324\)

Subtract 324 from both sides

\(576 = {width}^{2} \\ width = \sqrt{576} = 24 \: \: inches\)

Answer:

1/2 since there's always a fifty-fifty chance.

Answer: 50, 60, less.

Step-by-step explanation: The theoretical probability of the coin landing heads up is 50%

Based on​ Liz's results, the experimental probability of the coin landing heads up is 60%

The theoretical probability is Less  than the experimental probability in this experiment.

Hope this helped have a nice day!

Answer:

Step-by-step explanation:

-y+4=72

-y=72-4

-y=68

y=-68

-z-10+72=180

-z=180-62

-z=118

z=-118

-3x+6=-z-10

-3x=-6+118-10

-3x=102

-x=34

x=-34

The model used by Victor in the linear equation is incorrect,

The parameters are that;

Victor saved: $89.25

Cost of the bicycle = $129.85

Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;

$89.25 + x = $129.85

This can be expressed in words as;

The amount of money he already has saved + the amount of money he still requires = the total price of the bike.

An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle

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Complete question is;

Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.

89.25 + 129.85 = x

Does Victor's equation correctly model the problem?

p = 0

\(8 - 4(2p - 2) = 7 + p + 9\)

➡️ \(8 - 8p + 8 = 16 + p\)

➡️ \(16 - 8p = 16 + p\)

➡️ \( - 8p = p\)

➡️ \( - 8p - p = 0\)

➡️ \( - 9p = 0\)

➡️ \(p = 0\)

Answer:

-2.5?

Step-by-step explanation:

ANSWER

f(-4) = -21

EXPLANATION

We have that:

f(x) = 6x + 3

We want to find f(-4)

To do this, we replace x with -4:

f(-4) = 6(-4) + 3

f(-4) = -24 + 3

f(-4) = -21

That is the answer.

What is the question?

.

.

Visualize three non-coplanar lines intersecting at point J in three-dimensional space to represent the given scenario. Label the lines as AB, CD, and EF, with their common intersection point marked as J.

Imagine three lines in three-dimensional space intersecting at point J. These lines do not all lie in the same plane, meaning they are not coplanar. To represent this, envision a three-dimensional coordinate system and draw three non-coplanar lines intersecting at a common point J in space. You can label the lines as Line AB, Line CD, and Line EF, and mark the point of intersection as J. This setup would illustrate the described relationship.

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The complete question is:

Draw and label a figure for each relationship. Three lines intersect at point J but do not all lie in the same plane.

G is not true

Answer: b. False

Step-by-step explanation:

The term " correlation" defines the nature of the relationship between the two quantities.

The term "causation" defines the effect of one variable one the other.

They both are used to analyse the relationship between variables such that

Presence of causation implies there is correlation between variables but correlation does not imply causation.

So, correlation coefficient (r) has nothing to do with the cause.

That means having a good correlation of r = 0.71 between the time spent playing video games each week and grade point average for a group of high school boys doesn't imply that playing video games causes students to get lower grades.

Hence, the given statement is False.

Answer:

15504

Step-by-step explanation:

\( = {}^{20} C _{5} \\ = 15504\)

Therefore, the speed of the bike is approximately 12.61 miles per hour.

To calculate the speed of the bike, we first need to find the linear speed of the front gear. The linear speed of a rotating object is given by the formula v = rω, where v represents the linear speed, r is the radius, and ω is the angular velocity.

The front gear has a radius of 3.5 inches and is rotating at a rate of 65 rotations per minute. Since there are 2π radians in one rotation, the angular velocity can be calculated as ω = 65 * 2π = 130π radians per minute.

Now we can calculate the linear speed of the front gear using v = rω. Substituting the values, we have v = 3.5 * 130π = 455π inches per minute.

To convert the speed to miles per hour, we need to consider the back gear and the wheel. The back gear has a radius of 2.25 inches, and the wheel has a circumference of 2π * 14.0 inches = 28π inches.

Since the front gear is connected to the back gear, their linear speeds are equal. Therefore, the linear speed of the back gear is also 455π inches per minute.

To convert the linear speed to miles per hour, we divide by the number of inches in a mile (12 * 5280) and multiply by the number of minutes in an hour (60). Hence, the speed of the bike is (455π * 60) / (12 * 5280) ≈ 12.61 miles per hour.

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To find the common ratio and the first four terms of the geometric sequence {(9^n+2)/(3)}, let's first rewrite the given expression to make it easier to understand i.e. Term a_n = (9^n+2)/3

Now, let's find the first four terms:
a_1 = (9^(1)+2)/3 = (9+2)/3 = 11/3
a_2 = (9^(2)+2)/3 = (81+2)/3 = 83/3
a_3 = (9^(3)+2)/3 = (729+2)/3 = 731/3
a_4 = (9^(4)+2)/3 = (6561+2)/3 = 6563/3

The first four terms are:
a_1 = 11/3
a_2 = 83/3
a_3 = 731/3
a_4 = 6563/3

To find the common ratio, divide the second term by the first term (or any consecutive terms):
Common ratio = a_2 / a_1 = (83/3) / (11/3) = 83/11 = 3

So, the common ratio is indeed 3, and the first four terms are 11/3, 83/3, 731/3, and 6563/3.

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Answer:

The answer is: Hundred Thousands

Answer:

The inequality x + 3 < 12 can be used to determine the number of miles left to jog.

Step-by-step explanation:

It is given that:

Number of miles Beth has already jogged = 3 miles

She plans to join less than 12 miles.

Let,

x represent the number of miles left to jog.

x + 3 < 12

x + 3 - 3 < 12 - 3

x  < 9

Therefore,

The inequality x + 3 < 12 can be used to determine the number of miles left to jog.

Answer:

−22

Answer:  8

Step-by-step explanation:

distributive property = -18 + 3r = 6

cross river = 3r = 6 + 18

add = 3x = 24

lastly, divide = 8

C - The growth rate tells the rate at which the population is growing at time t = 20 is the correct answer.

(a) Find the growth rate, dt The given expression for population growth in the city is P(t) = 500,000 + 1000t².To find the growth rate, we differentiate P(t) w.r.t. t. dP/dt = d/dt (500,000 + 1000t²) = 2000tThe growth rate is 2000t.

(b) Find the population after 20 yr.To find the population after 20 years, we need to find P(20). P(t) = 500,000 + 1000t²Putting t = 20, P(20) = 500,000 + 1000(20)² = 3,700,000(c) Find the growth rate at t = 20.The growth rate at t = 20 is 2000t, where t = 20. So, the growth rate at t = 20 is 40,000.(d) Explain the meaning of the answer to part

(c).The growth rate at t = 20 tells us the rate at which the population is growing at that particular point in time. The population growth rate at t = 20 is 40,000 people per year, which means the city is growing rapidly at that particular point in time.

Therefore, option C - The growth rate tells the rate at which the population is growing at time t = 20 is the correct answer.

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a) The critical value of z at the 0.05 level of significance for a one-tailed test is 1.645

b) The null and alternative hypotheses are

Null hypothesis: H0: p ≤ 0.59

Alternative hypothesis: Ha: p > 0.59

The null hypothesis is that the proportion of readers who own a personal computer is equal to or less than 59%. The alternative hypothesis is that the proportion of readers who own a personal computer is greater than 59%.

H0: p ≤ 0.59

Ha: p > 0.59

To test this hypothesis, we can use a one-tailed z-test for a proportion. We would collect a random sample of newsletter readers and determine the proportion of them who own a personal computer. We would then calculate the test statistic z using the formula:

z = (P - p₀) / sqrt(p₀×  (1 - p₀) / n)

where P is the sample proportion, p₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.

If the calculated z-value is greater than the critical value obtained from a standard normal distribution table at the 0.05 level of significance, we would reject the null hypothesis in favor of the alternative hypothesis.

Therefore, the decision rule for this test can be expressed as follows

If z > 1.645, reject H.

Otherwise, fail to reject H0.

Note that the critical value of z at the 0.05 level of significance for a one-tailed test is 1.645.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Then, according to the normal table, the probability of gettin z < 0.18 is given by the area on the left of z = 0.18 in the graph related to the distribution. Then we have: P (z < 0.18) = 0.5714

Answer:

keep adding 35 to the graph

Step-by-step explanation:

Answer:here’s the table

Step-by-step explanation:

Celina -3

Jannie 3

Sami 1

Ted 4

Travis ??

Answer:

Step-by-step explanation:

-5