Sandy cut three pieces of yarn to use for her art project one was 1ft 8in long one was 10 in long and one was 2 ft 6 in Long how much yarn did Sandy use

Answer:

x=1

Step-by-step explanation:

6^2x- 3 = 6^-2x+1

Since the bases are the same, the exponents are the same

2x-3 = -2x+1

Add 2x to each side

2x-3+2x = -2x+1+2x

4x-3 = 1

Add 3 to each side

4x-3+3 = 1+3

4x = 4

Divide each side by 4

4x/4 = 4/4

x=1

Answer: C. x = 1

Explanation: E21

Answer:

  55.2 gallons/day

Step-by-step explanation:

There are 2.4 ten-hour periods in one day, so the total number of gallons per day is ...

  (2.4 periods/day)(23 gallons/period) = 55.2 gallons/day

Answer:

Center = ( 1,-2)

radius = 2

Answer:

^D

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

12.5/5=2.5

2(2.5)+2*5=

5+10=15

Final answer:

To calculate the perimeter of the park with an area of 12.5 sq miles and a width of 5 miles, you divide the area by the width to get the length and then apply the formula P = 2(l + w). The perimeter of the park is 15 miles.

Explanation:

The question pertains to finding the perimeter of a park given its area and width. To find the perimeter, we need to know both the length and the width of the park. Since the area of the park is 12.5 sq miles and the width is 5 miles, we can find the length by dividing the area by the width, which gives us a length of 2.5 miles. Once we have both dimensions, we can use the formula for perimeter P = 2(l + w), where l is the length and w is the width.

Using the formula, the perimeter P = 2(2.5 miles + 5 miles) = 2(7.5 miles) = 15 miles. So, the perimeter of the park is 15 miles.

Final answer:

To estimate the number of students who took a geometry test based on certain scores and parameters, consider the range of scores and standard deviations to make the calculation.

Explanation:

The question:
The student is asking to estimate the number of students who took a geometry test given certain scores and parameters.

Step-by-step explanation:

Answer:

A wide variety of life exists in Florida Panhandle

Step-by-step explanation:

A habitat is the natural environment in which organisms lives. We have three types of habitat which include aquatic, terrestrial and arboreal. These habitats contains different organisms.

Florida Panhandle having almost sixty different types of habitats means more organisms living in this place. This translates to a wide variety of life existing in Florida Panhandle.

The statement that best describes the Florida Panhandle based on the fact that it has almost 60 different types of habitats is that it is a region with high biodiversity and a variety of ecosystems.

The presence of nearly 60 distinct habitats in the Florida Panhandle indicates a rich tapestry of ecological systems. Biodiversity refers to the variety of life in the world or in a particular habitat or ecosystem. This includes the different species of plants, animals, and microorganisms, the genetic differences among them, and the ecosystems in which they occur. A high number of habitats suggests that the area supports a wide range of species that have adapted to the different environmental conditions present in these habitats.

Ecosystems are communities of living organisms in conjunction with the nonliving components of their environment (things like air, water, and soil), interacting as a system. These ecosystems can range from coastal marshes and estuaries to longleaf pine forests and freshwater springs. Each habitat type provides unique resources and living conditions, which in turn support different types of organisms.

The Florida Panhandle's diverse habitats likely result from its geography, climate, and history. The region may include coastal areas, wetlands, forests, and other landscapes, each with its own set of habitats. This diversity is crucial for the overall health of the environment, as it allows for a greater number of species to thrive and for ecological processes to function effectively. It also provides opportunities for recreation, research, and education, and it underscores the importance of conservation efforts to protect these valuable natural resources.

In summary, the high number of habitats in the Florida Panhandle is indicative of its ecological richness and the importance of conserving this diversity for environmental health and human enjoyment."

Answer:

The centre is the point (-4,6).

The length of the radius is 14.

Step-by-step explanation:

The equation of a circle has the following format:

[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]

In which r is the radius and the centre is the point [tex](x_{0}, y_{0})[/tex]

In this question:

We have to complete the squares, to place the equation in the general format:

So

[tex]x^{2} + 8x + y^{2} - 12y = 144[/tex]

To complete the quares, we divide each first order term(8 and -12) by two, having two new terms(4 and -6). With this, we write as the square of (x+4) and (y-6). To compensate, we have to find the square of 4 and -6 on the other side of the equality.

[tex](x+4)^{2} + (y-6)^{2} = 144 + (4)^{2} + (-6)^{2}[/tex]

[tex](x+4)^{2} + (y-6)^{2} = 196[/tex]

The centre is the point (-4,6).

The length of the radius is [tex]\sqrt{196} = 14[/tex]

The center and the length of the radius of the circle is (-4, 6) and 14units respectively

The standard equation of a circle is expressed as:

x^2+y^2+2gx+2fy+c = 0

where:

C = (-g, -f)

r = √g²+f²-c

Given the equation of a circle expressed as:

x^2 + 8x + y^2 - 12y = 144.

Compare both equations

2gx = 8x
g = 4

2fy = -12y

y = -6

The centre of the circle will be at (-4, 6)

Determine the radius

r = √4²+6²+144
r = 14

Hence the center and the length of the radius of the circle is (-4, 6) and 14units respectively

Learn more on the equation of a circle here: https://brainly.com/question/1506955

Answer:

We conclude that less than 90% of all orders are mailed within 72 hours after they are received.

Step-by-step explanation:

We are given that the company claims that at least 90% of all orders are mailed within 72 hours after they are received.

A recently taken sample of 150 orders showed that 115 of them were mailed within 72 hours.

Let p = proportion of orders that are mailed within 72 hours after they are received.

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 90%      {means that at least 90% of all orders are mailed within 72 hours after they are received}

Alternate Hypothesis, [tex]H_A[/tex] : p < 90%      {means that less than 90% of all orders are mailed within 72 hours after they are received}

The test statistics that would be used here One-sample z proportion statistics;

                    T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of orders that were mailed within 72 hours = [tex]\frac{115}{150}[/tex] = 0.767

           n = sample of orders = 150

So, test statistics  =  [tex]\frac{0.767-0.90}{\sqrt{\frac{0.767(1-0.767)}{150} } }[/tex]  

                              =  -3.853

The value of z test statistics is -3.853.

Now, at 2.5% significance level the z table gives critical value of -1.96 for left-tailed test. Since our test statistics is less than the critical values of z as -3.853 < -1.96, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that less than 90% of all orders are mailed within 72 hours after they are received.

Answer:

1165.73 sq.cm. of newspaper are  needed to cover the lateral areas of all five sculptures

Step-by-step explanation:

Diameter of 1 sculpture = 9 cm

Radius of 1 sculpture =[tex]\frac{9}{2}=4.5 cm[/tex]

Slant height of sculpture = l = 16.5 cm

Lateral surface area of each sculpture = [tex]\pi r l = \frac{22}{7} \times 4.5 \times 16.5 =233.3571 cm^2[/tex]

Lateral surface area of 5 sculptures =[tex]233.3571 \times 5 =1165.73 cm^2[/tex]

Hence 1165.73 sq.cm. of newspaper are  needed to cover the lateral areas of all five sculptures

Answer:

1,165.73 cm^2

Step-by-step explanation:

Answer:

See attached image for a balanced one by adding a row

Final answer:

The question involves converting an unbalanced transportation problem for Major Motors into a balanced one and solving it using the Greedy Heuristic. It requires adding a dummy destination with zero shipping cost and then allocating the supply to demand sites starting from the lowest shipping costs.

Explanation:

The student's question pertains to creating a balanced transportation problem from the given unbalanced scenario involving Major Motors and using the Greedy Heuristic to find a solution. The three plants located in Flint, Fresno, and Monterrey have production capacities of 43, 26, and 31 (in hundreds of cars) respectively, and the distribution centers in Phoenix, Davenport, and Columbia have requirements of 26, 28, and 30 (in hundreds of cars) respectively.

First, we need to balance the problem by equating total supply with total demand. The total supply from all plants is 43 + 26 + 31 = 100 (in hundreds of cars), and the total demand from all distribution centers is 26 + 28 + 30 = 84 (in hundreds of cars). We will need to add a dummy distribution center with a demand of 16 (in hundreds of cars) to balance the problem, with zero shipping cost to this dummy destination from all plants. Now, we apply the Greedy Heuristic, which involves selecting the lowest cost choices first and fulfilling demand as supply allows.

We start by assigning cars to the distribution centers from the cheapest shipping options available. Let's illustrate a step, shipping from Flint to Columbia as it has the lowest cost of $7,000 for 100 cars. Continuing this process until all demands are met will provide us with an approximate solution to the transportation problem.

Answer:

3/4

Step-by-step explanation:

We know a geometric sequence has the formula:  a_n = a_1 * r^(n-1)

a_2 = 20

a_4 = (45/4)

so...    a_2 = a_1* r^(2-1) =  20

and    a_4 = a_1* r^(4-1) = (45/4)

a_1 * r = 20

a_1* r^3 = (45/4)

a_1 = 20/r

(20/r) * r^3 = (45/4)

20 * r*r = 45/4

r*r = 45/80 =  9/16

r =  3/4   or  r = -3/4   it must be positive.

common ratio is r = 3/4

Answer:

see below

Step-by-step explanation:

This problem could have 2 solutions

We could be given two legs

a^2 + b^2 = c^2

5^2 +13^2 = c^2

25+169 = c^2

194 = c^2

Taking the square root on each side

sqrt(194) = c

Or the 13 could be the hypotenuse

a^2 + 5^2 = 13^2

a^2 +25 = 169

a^2+25-25 = 169-25

a^2 = 144

Taking the square root of each side

a = 12

Answer:

  {-5, -4, -2, 0, 1}

Step-by-step explanation:

The domain is the list of first numbers of the ordered pairs. That list is shown above.

LUMBERJACKS: 4,989,600 arrangements. HIGHLIGHT: 362,880 arrangements. COOKBOOK: 10,080 arrangements. [tex]\( \frac{{88!}}{{86!}} = 7656 \).[/tex]

To find the number of unique arrangements for each word:

1. LUMBERJACKS:

  - Total letters: 11

  - Since there are repeated letters (U, B, E), we need to account for that.

  - The formula for permutations of a word with repeated letters is [tex]\( \frac{{n!}}{{n_1! \times n_2! \times \ldots \times n_k!}} \), where \( n \) is the total number of letters and \( n_1, n_2, \ldots, n_k \)[/tex] are the counts of each distinct letter.

  - For LUMBERJACKS, we have:

    - 2 L's

    - 2 M's

    - 2 B's

  - So, the number of unique arrangements is[tex]\( \frac{{11!}}{{2! \times 2! \times 2!}} \).[/tex]

2. HIGHLIGHT:

  - Total letters: 9

  - There are no repeated letters.

  - So, the number of unique arrangements is simply [tex]\( 9! \).[/tex]

3. COOKBOOK:

  - Total letters: 8

  - There are repeated letters (O, K).

  - For COOKBOOK, we have:

    - 2 O's

    - 2 K's

  - So, the number of unique arrangements is [tex]\( \frac{{8!}}{{2! \times 2!}} \).[/tex]

4. [tex]\( \frac{{88!}}{{86!}} \)[/tex]:

  - This expression simplifies to [tex]\( 88 \times 87 \), as \( 86! \) cancels out. - So, \( 88! \) divided by \( 86! \) equals \( 88 \times 87 \).[/tex]

Let's compute these:

1. For LUMBERJACKS:

[tex]\[ \frac{{11!}}{{2! \times 2! \times 2!}} = \frac{{39916800}}{{8}} = 4989600 \][/tex]

2. For HIGHLIGHT:

[tex]\[ 9! = 362880 \][/tex]

3. For COOKBOOK:

[tex]\[ \frac{{8!}}{{2! \times 2!}} = \frac{{40320}}{{4}} = 10080 \][/tex]

[tex]4. For \( \frac{{88!}}{{86!}} \):[/tex]

[tex]\[ 88 \times 87 = 7656 \][/tex]

Answer:

B. 9

Step-by-step explanation:

We know that a full circle should equal 360°, that'll help!

Since the 140°+3x+13 should equal to 180, because that makes the half of the circle it covers, we know how to set up our equation!

It should look like this:

3x+13=40

ISOLATE YOUR VARIABLE:

- Subtract 13 from both sides

NEXT, CONTINUE ISOLATING:

3x=27

- Divide by 3 from both sides.

FINALLY:

You will get X=9!

Answer:

36.58% probability that one of the devices fail

Step-by-step explanation:

For each device, there are only two possible outcomes. Either it fails, or it does not fail. The probability of a device failling is independent of other devices. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

A total of 15 devices will be used.

This means that [tex]n = 15[/tex]

Assume that each device has a probability of 0.05 of failure during the course of the monitoring period.

This means that [tex]p = 0.05[/tex]

What is the probability that one of the devices fail?

This is [tex]P(X = 1)[/tex]

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

[tex]P(X = 1) = C_{15,1}.(0.05)^{1}.(0.95)^{14} = 0.3658[/tex]

36.58% probability that one of the devices fail

Using the a TI-84 calculator, the expression is:

binomcdf(500, 0.5, 350)

The probability of having a or fewer successes, in n binomial trials, each with a p probability of successes is found according to the following expression:

binomcdf(n,p,a)

In this problem:

Then, the expression is:

binomcdf(500, 0.5, 350)

A similar problem is given at https://brainly.com/question/2912622

Answer:

There is not enough evidence to reject the null hypothesis.

Step-by-step explanation:

(a)

The hypothesis can be defined as follows:  

H₀: p₁ - p₂ ≤ 0 vs. Hₐ: p₁ - p₂ > 0.  

(b)

The test statistic is defined as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

The information provided is:

n₁ = 244

n₂ = 311

x₁ = 122

x₂ = 137

Compute the sample proportions and total proportions as follows:

[tex]\hat p_{1}=\frac{x_{1}}{n_{1}}=\frac{122}{244}=0.50\\\\\hat p_{2}=\frac{x_{2}}{n_{2}}=\frac{137}{311}=0.44\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{122+137}{244+311}=0.47[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

    [tex]=\frac{0.50-0.44}{\sqrt{0.47(1-0.47)[\frac{1}{244}+\frac{1}{311}]}}\\\\=1.41[/tex]

The test statistic value is 1.41.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level α = 0.05.

Compute the p-value as follows:

 [tex]p-value=P(Z>1.41)\\=1-P(Z<1.41)\\=1-0.92073\\=0.07927\\\approx 0.08[/tex]

*Use a z-table.

The p-value of the test is 0.08.

p-value = 0.08 > α = 0.05

The null hypothesis will not be rejected at 5% significance level.

Thus, there is not enough evidence to reject the null hypothesis.

Answer:

i) The sketch of the area under the normal distribution curve is attached to this solution of the question.

ii) The minimum number of seconds we could expect the longest 20% of customers to wait in line = 162 seconds.

Step-by-step explanation:

This is is a normal distribution problem with

Mean = μ = 138 seconds

Standard deviation = σ = 29 seconds

i) Which of the following illustrates the shaded area under the normal distribution for the top 20%?

We first obtain the z-score that corresponds to the lower limit of the top 20% of the distribution of waiting times.

Let that z-score be z'

P(z > z') = 0.20

P(z > z') = 1 - P(z ≤ z') = 0.20

P(z ≤ z') = 1 - 0.20 = 0.80

P(z ≤ z') = 0.80

So, checking the normal distribution table,

z' = 0.842

we can then go ahead and obtain the waiting time that corresponds to this z-score.

Let the waiting time that corresponds to this z-score be x'

z' = (x' - μ)/σ

0.842 = (x' - 138)/29

x' = 162.42 seconds

Since, the options for the shaded area under the normal curve isn't presented with this question, the graph of the shaded area under the normal curve that corresponds to the top 20% waiting times is attached to this solution.

ii) What is the minimum number of seconds we could expect the longest 20% of customers to wait in line?

The minimum number of seconds we could expect the longest 20% of customers to wait in line corresponds to the lower limit of the top 20% waiting times obtained in (i) above.

The minimum number of seconds we could expect the longest 20% of customers to wait in line = 162.42 seconds = 162 seconds to the nearest second

Hope this Helps!!!

The zeros of the quadratic function f(x) = 2x² + 16x - 9 are obtained by using the quadratic formula, resulting in x = -4 + √{82} and x = -4 - √{82}.

To find the zeros of the quadratic function f(x) = 2x² + 16x - 9, we can either factor the quadratic, complete the square, or use the quadratic formula. The function provided is already in the standard form of a quadratic equation, ax² + bx + c = 0. For this equation, a = 2, b = 16, and c = -9.

To use the quadratic formula, x = (-b√{b² - 4ac}) / (2a), we substitute the values of a, b, and c into the formula:

x = (-(16) √{(16)² - 4(2)(-9)}) / (2(2))
x = (-16 √{256 + 72}) / 4
x = (-16 √{328}) / 4
x = (-16 √{82}) / 4
x = -4 √{82}

Therefore, the zeros of the function are x = -4 + √{82} and x = -4 - √{82}.

Answer: Option D, (40 minutes) is the correct answer.

Step-by-step explanation: Time she has to complete 3 assignments = 2 hours.

Let the time taken to complete each assignment be 'x'

→ 2 hours = 120min

∴ The amount spend for each assignment is the same.

∴ Time taken for each assignment = 120/3 = 40min

∴ It takes 40 min to complete each assignment, Option D.

Answer:

The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.

Step-by-step explanation:

The area of the parallelogram is given by the following expression:

[tex]A = \|\vec u\times \vec v\|[/tex]

The vectors are, respectively:

[tex]\vec u = (10-2, 1 - 1,0-0)[/tex]

[tex]\vec u = (8,0,0)[/tex]

The base of the parallelogram is 8 units.

[tex]\vec v = (8-2, 4-1,0-0)[/tex]

[tex]\vec v = (6,3,0)[/tex]

The height of the parallelogram is 3 units.

The cross product of both vectors is:

[tex]\vec u \times \vec v = (0,0,24)[/tex]

The area of the parallelogram is given by the norm of the resulting vector:

[tex]\|\vec u \times \vec v\| = 24[/tex]

Answer:

To find the two consecutive natural numbers that sum up to 13, we set up an equation: x + (x+1) = 13. Solving this, we find that x = 6, and the next number is x + 1 = 7. Therefore, the numbers are 6 and 7.

Let's call the natural number x. According to the problem, the sum of x and the next number (x+1) is 13. To find the values of these numbers, we can set up the following equation:

x + (x + 1) = 13

Simplifying the equation, we combine like terms to get:

2x + 1 = 13

Subtract 1 from both sides:

2x = 12

Divide both sides by 2:

x = 6

Now that we have the value of x, we can find the next number:

x + 1 = 6 + 1 = 7

So the two consecutive natural numbers that sum up to 13 are 6 and 7.

Answer: according to my calculations the answer is (3,-2) if im wrong im sorry but thats what i got  

Step-by-step explanation:

The solution in the attached below that is point (2, 1).

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. A set of such values is called a solution set to the considered equation or inequality.

we have given that the linear inequality y < Negative one-half + 2

y < - 1x/2 + 2

The solution of the inequality is the shaded area below the dashed line;

y = - 1x/2 + 2

The slope of the dashed line is negative 1/2.

The y-intercept of the dashed line is the point (0,2) and the x-intercept of the dashed line is the point (4,0).

The solution is attached below.

Noted that Any point that lies on the shaded area is a solution to the inequality and if a point is a solution to the linear inequality, then the point must satisfy the inequality.

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Answer:

P = 1/216

the probability that you would roll 3 sixes is 1/216

Step-by-step explanation:

For a given dice, there are six possibilities.

We have;

1,2,3,4,5,6

The probability of rolling a six(6) is;

P(6) = 1/6

Then, the probability of rolling 3 sixes is a multiple of the P(6), given as;

P = P(6) × P(6) × P(6)

P = 1/6 × 1/6 × 1/6

P = 1/216

the probability that you would roll 3 sixes is 1/216

The probability of getting 3 sixes in 4 dice rolls is A. [tex]\( \frac{5}{216} \)[/tex].

To find the probability of rolling exactly 3 sixes with 4 dice rolls using the slot method, we'll analyze several cases:

Step 1 :

Case 1: Three sixes in the first three rolls, any number on the fourth roll.

Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} \).[/tex]

Case 2: Two sixes in the first two rolls, one six on the third roll, any number on the fourth roll.

Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} \).[/tex]

Case 3: One six in the first roll, two sixes in the next two rolls, any number on the fourth roll.

Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} \).[/tex]

Case 4: One six in the last roll, three sixes in the first three rolls.

Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \).[/tex]

Step 2 :

Now, sum the probabilities from all cases:

Total probability [tex]\(= \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} + \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} + \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} + \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \).[/tex]

This simplifies to [tex]\( \frac{15}{216} + \frac{1}{216} = \frac{16}{216} = \frac{2}{27} \).[/tex]

Thus, the correct option is A. [tex]\( \frac{5}{216} \), as \( \frac{2}{27} \)[/tex] is equivalent to [tex]\( \frac{5}{216} \)[/tex].

Complete Question :

Question:

Using the slot method and considering multiple cases, calculate the probability of rolling exactly 3 sixes with 4 dice rolls.

A. [tex]\( \frac{5}{216} \)[/tex]

B. [tex]\( \frac{25}{216} \)[/tex]

C. [tex]\( \frac{45}{216} \)[/tex]

D. [tex]\( \frac{125}{1296} \)[/tex]

Answer:

m Arc AD = 43°

Step-by-step explanation:

The question is missing a diagram. Find attached the diagram of the question.

Given:

AB is a diameter of circle P

Solution:

From the diagram,

∠ADP = 7x+1

∠BPC = 9x-7

∠CPD = 90° (the symbol of right angle is drawn)

∠m Arc APB = 180° (sum of angles on a straight line or sum of angle in a semi circle)

∠APD + ∠CPD + ∠BPC = 180°

(7x+1)° + 90° + (9x-7)° = 180°

7x+1 + 90 + 9x-7 = 180

Collect like terms

7x+9x = 180 - 90 + 7 -1

16x = 96

x = 96/16

x = 6

Insert the value color x in ∠APD

∠APD = 7(6) + 1

∠APD = 43°

m Arc AD = ∠ APD

m Arc AD = 43°

Therefore arc measure of AD in degrees = 43°

The answer is A. Log 9 5

I got it right on ed .

The value of the expression log₉10-log₉(1/2)-log₉4 is log₉5.

An expression is combination of variables, numbers and operators.

The given expression is

log₉10-log₉(1/2)-log₉4

if we observe the base of logs are same

so, we can use property of logarithms

[tex]log_{a} b+log_{a} c=log_{a} bc[/tex]

log₉10-log₉(1/2×4)

Now we use the property of logarithms of subtraction.

log₉10-log₉(2)

log₉(10/2)

log₉5

Hence, the value of the expression log₉10-log₉(1/2)-log₉4 is log₉5.

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Maria's test score is calculated by dividing the number of correct answers (22) by the total number of questions (25) and then multiplying by 100, resulting in a score of 88%.

Maria took a history test with 25 questions and correctly answered 22 questions. To find her test score as a percent, you divide the number of correct answers by the total number of questions and then multiply the result by 100. So, Maria's score would be (22 correct answers / 25 total questions) × 100 = 88%.

This is how it calculates:

First, write the number of correct answers over the total number of questions as a fraction: 22/25.

Then, convert this fraction to a decimal by dividing 22 by 25, which equals 0.88.

Finally, multiply the decimal by 100 to get the percentage. So, 0.88 × 100 equals 88%.

Maria's test score expressed as a percent is 88%.

Answer:28.5

Step-by-step explanation: