Spiral Review Gretchen is delivering boxes of cookies to her neighbors. Her wagon itself weighs 12 pounds when empty and will hold up to 9 boxes.
If each box of cookies weighs 1 pound, what is the range of the total weight of her wagon while she is delivering cookies?
Enter the correct answers in the boxes.


Answer:

The least number of stamps required is \(9\)

Step-by-step explanation:

Let the number of \(3\) cent stamps be \(x\) and \(4\) cent stamps be \(y\)

We have

\(3x+4y=33\)

The minimum number is obtained when more  \(4\) cent stamps are used

Here \(y\) cannot be greater than \(8\) since \(\frac{33}{4} <9\)

Substitute \(y=8\)

\(3x+4\times 8=33\\\\3x=1\\\\x=\frac{1}{3}\)

Not possible since \(x\) is not a fraction

Substitute \(y=7\)

\(3x+4\times 7=33\\\\3x=5\\\\x=\frac{5}{3}\)

Not possible since \(x\) is not a fraction

Substitute \(y=6\)

\(3x+4\times 6=33\\\\3x=9\\\\x=\frac{9}{3}\\\\=3\)

Possible

Hence minimum number of stamps is

\(=x+y\\\\=3+6\\\\=9\)

Let's assume that Mr. and Mrs. Johnson bought x adult tickets and y children's tickets.

Since there are three children, we know that:

y = 3x

The total cost of the parents' tickets is 7x, and the total cost of the children's tickets is 4y. Substituting y = 3x, we get:

total cost of parents' tickets = 7x

total cost of children's tickets = 4(3x) = 12x

Therefore, the ratio of the total cost of the parents' tickets to the total cost of the children's tickets is:

(7x) / (12x) = 7/12

So the answer is 7/12, which cannot be simplified further. Therefore, the ratio is 7/12, which can be written in the form aib as 0+7/12i.

Answer: 7:6

Step-by-step explanation:

1. There are two adults (Mr. and Mrs. Jonhson) and three children. So let's make adults = y and children = x

2. Adult tickets cost $7. So we are going to multiply 7 x 2y = $14

3. Children's tickets cost $4. So we are going to multiply 4 x 3x = $12

4. The last step is to fully reduce \(\frac{14}{12}\) = \(\frac{7}{6}\)

5. So the answer is 7:6

Answer: 4.12

Step-by-step explanation: 4.12 x 4.12=17

Answer:

4.123

Step-by-step explanation:

Have a great day

Answer:

16+24=40

Step-by-step explanation: 2x+5(y-1) when x=8 and y=5. put x where it belongs, by the 2 and do the same with y, by the -1. and then slove. 2*8= 16 , 5*5= 25-1, then add 16 and 24 together and get 40.

Step-by-step explanation:

We know that if an arc subtends an angle of theta , with a radius r , then the measure of arc is r× theta . Here theta is 109° .

\(\implies l = r\theta \\\\\implies l = r\times 109^{\circ}\\\\\implies l = r \times \dfrac{109}{180}\pi rad \\\\\implies \boxed{\boxed{ l = 0.6\pi r m }}\)

where r will be the radius .

The interval for which the graph remains constant is; Option C: -4 ≤ x ≤ -2

The interval on the graph at which it is constant would be the x-interval where the value of y remains the same.

Now, from the given graph, we can see that from x = -2 to x = -4, the value of y remains the same at y = -3.

Thus, we can conclude that the interval for which the graph remains constant is; -4 ≤ x ≤ -2

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Answer:

18  ft

Step-by-step explanation:

Answer:

The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north.

Step-by-step explanation:

• To find the magnitude of the resultant vector, we have to use Pythagoras's theorem:

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

where:

a ⇒ hypotenuse (= resultant vector = ? mi)

b, c ⇒ the two other sides of the right-angled triangle (= 452 mil North, 767 mi West).

Using the formula:

resultant² = \(452^2 + 767^2\)

⇒ resultant =  \(\sqrt{452^2 + 767^2}\)

⇒ resultant = 890.3 mi

• To find the direction, we can find the angle (labeled x in diagram) that the resultant makes with the north direction:

\(tan (x) =\frac{767}{452}\)

⇒ \(x = tan^{-1} (\frac{767}{452} )\)

⇒ \(x = \bf{59.5 \textdegree}\)

∴ The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north .

Answer:

\(\displaystyle Approximately\:59°\:at\:a\:magnitude\:of\:approximately\:890\:miles\)

Step-by-step explanation:

\(\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:\theta \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:\theta \\ \frac{OPPOCITE}{ADJACENT} = tan\:\theta \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:\theta \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:\theta \\ \frac{ADJACENT}{OPPOCITE} = cot\:\theta\)

We must use trigonometry to help us find the direction of the aeroplane's resultant vector. Do as I do:

\(\displaystyle \frac{452}{767} = cot\:x \hookrightarrow cot^{-1}\:\frac{452}{767} = x; 59,488772482...° = x \\ \\ \boxed{59° \approx x}\)

Now, we will use the Pythagorean Theorem to find the magnitude of the aeroplane's resultant vector. Do as I do:

\(\displaystyle a^2 + b^2 = c^2 \\ \\ 767^2 + 452^2 = c^2 \\ \sqrt{792593} = \sqrt{c^2}; 890,27692321... = c \\ \\ \boxed{890 \approx c}\)

Therefore, the direction and magnitude of the aeroplane's resultant vector are approximately eight hundred ninety miles at an angle of elevation of fifty-nine degrees.

I am joyous to assist you at any time.

We shall begi by determining the size of the arc that was cut out of the rectangular paperboard.

Observe that the new shape now consists of two lengths measuring 23 inches each, and one width measuring 18 inches, and the half circumerence measuring 28.26 inches.

The perimeter therefore is the addition of all sides and that is;

Perimeter = 23 + 23 + 18 + 28.26

Perimeter = 92.26 inches

"Meta Analysis" is a quantitative statistical analysis that compares and combines the results of individual but similar studies.

A quantitative statistical analysis of numerous distinct but related experiments or research to assess the statistical significance of the pooled results.

Some characteristics of meta analysis are-

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The probability of rolling the same number on all three dice can be found by multiplying the probabilities of rolling the same number on each individual die. The probability of rolling the same number on the 6-sided die is 1/6, the probability of rolling the same number on the 8-sided die is 1/8, and the probability of rolling the same number on the 12-sided die is 1/12. Multiplying these probabilities together gives us the probability of rolling the same number on all three dice: (1/6) * (1/8) * (1/12) = 1/576.

The probability of rolling a "4" on one of the dice and it being the 6-sided die can be found by multiplying the probability of rolling a "4" on the 6-sided die (1/6) by the probability of picking the 6-sided die at random (1/3). This gives us a probability of (1/6) * (1/3) = 1/18.

The probability of the smallest number rolled being at least 3 can be found by subtracting the probability of the smallest number being less than 3 from 1. The probability of the smallest number being less than 3 is the probability of rolling a 1 or a 2 on each of the dice: (2/6) * (2/8) * (2/12) = 1/72. Therefore, the probability of the smallest number being at least 3 is 1 - (1/72) = 71/72.

The probability of the product of the three numbers rolled being even can be found by subtracting the probability of the product being odd from 1. The probability of the product being odd is the probability of rolling an odd number on each of the dice: (3/6) * (4/8) * (6/12) = 1/8. Therefore, the probability of the product being even is 1 - (1/8) = 7/8.

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Answer:

y=4/3x-1

Step-by-step explanation:

Slope-intercept form: y=mx+b where m is slope and b is y-intercept

We can see that the y-intercept is (0,-1)

The slope is (3-(-1))/(3-0)=4/3

Answer:

78732

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

because 24 is the highest between those two

Answer:

24

Step-by-step explanation:

GCF of 48 and 72 Examples

Therefore, the greatest common factor of 48 and 72 is 24.

Considering that it has an outlier, the correct option regarding the most appropriate measure for the data-set is:

a. Median: 1.5.

For this problem, 14 is an outlier, hence the median should be used.

The ordered data-set is given by:

0, 0, 1, 1, 2, 2, 2, 14

The data-set has an even cardinality of 8, hence the median is the mean of the 4th and 5th elements, so:

Median = (1 + 2)/2 = 3/2 = 1.5.

Hence the correct option is:

a. Median: 1.5.

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Answer:

23 /12

1.916

Step-by-step explanation:

Answer:

1.- 140 in²

2.- 2.25 in²

3.- 43.25 in²

4.- 7.5 in²

5. 349.75 in²

Step-by-step explanation:

4 congruent triangles mean 4 triangles same measurement

area 1 triangle=(B*H)/2=(10*7)/2=35in²

for area of the roof are 4 by area 1 triangle=4*35=140 in²

2.- area hole. Hole is a square so area Is side by side

area=1.5*1.5=2.25

3.- area front except the hole. As the side of front is isosceles trapezoide which it’s area is (B1+B2)H/2 where B1=8 in and B2=5 in and H=7 in

so arera with hole=(8+5)*7/2=45.5 in²

Answer:

i cant see it clearly

Step-by-step explanation:

In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.

The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.

Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.

Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.

By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.

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The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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Answer:

x = 1

y = 2

Step-by-step explanation:

Solve by substitution

1) Solve for x in 7x + 8y = 23

x = 28 - 8y/7

2) Substitute x = 23-8y/7 into 8x - 4y = 0

8(23-8y)/7 - 4y = 0

3) Solve for y in 8(23-8y)/7 - 4y = 0

y = 2

4) Substitute y = 2 into x = 23-8y/7

x = 1

5) Therefore,

x = 1

y = 2

\(7x+8y -23=0 ~~~\\\\8x-4y+0 =0\\\\\text{Using cross multiplication method,}\\\\\\\dfrac{x}{8(0)- (-23)(-4)} = \dfrac{y}{8(-23) -7(0)} = \dfrac 1{7(-4) - (8)(8)}}\\\\\\\implies \dfrac x{0-92} = \dfrac y{-184-0} =\dfrac 1{-28 -64}\\\\\\\implies -\dfrac x{92} = -\dfrac{y}{184} = - \dfrac 1{92}\\\\\\\implies \dfrac{x}{92} = \dfrac y{184} = \dfrac 1{92}\\\\\text{Hence,}\\\\x= \dfrac{92}{92} = 1\\\\y= \dfrac{184}{92} = 2\)

Given :

Distance covered by object , D = 63 cm .

Time taken to cover distance D , t = 2 days .

To Find :

The speed of object in m/s .

Solution :

First we will convert all units into m and hours .

D = 63 cm = 0.63 m .

\(t=2\ days =2\times 24\ hours =48\ hours\) .

Now , speed is :

\(s=\dfrac{D}{t}\\\\s=\dfrac{0.63}{48}\ m/hours\\\\s=0.013\ m/hours\)

Hence , this is the required solution .

Answer:63

Step-by-step explanation:

The correct answer is C. A 95% confidence interval for μ will exclude the value 1.

A P-value of 0.072 means that if the null hypothesis (H0: μ = 1) is true, there is a 7.2% chance of obtaining a sample mean that is as extreme or more extreme than the one observed in the sample. This is not strong evidence against the null hypothesis at the 5% significance level (which is the standard level of significance used in hypothesis testing).

However, if we construct a 95% confidence interval for μ, we would expect the true population mean to fall within this interval 95% of the time if we were to repeat this study many times. Since the P-value is not less than 0.05, we fail to reject the null hypothesis at the 5% significance level.

Therefore, we can conclude that there is not enough evidence to suggest that the population mean is significantly different from 1.

However, a 95% confidence interval for μ will exclude the value 1, which means that we can be 95% confident that the true population mean is not equal to 1.

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There are 9 questions on the test.

Let, the number of multiple-choice questions on the test = m

the number of essay questions on the test = s

m + s = 26  .......(1)

So, We are also told that multiple choice is worth 3 points each, so the total number of points for m questions will be 3m.

As essays are worth 8 points each, so the total number of points for s questions will be 8s.

3m + 8s = 123 .......(2)

Now we will use the substitution method to solve a system of linear equations.

From equation (1) we will get,

m = 26 -s

Substituting this value in equation (2) we will get,

3 * (26- s) + 8s =123

78 - 3s + 8s = 123

5s = 123 -78

5s = 45

s = 45/5 = 9

So, there are 9 questions on the test.

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The complete question is:

Ada’s history teacher wrote a test for the class.

The test is 26 questions long and is worth 123 points.

Ada wrote two equations, where m represents the

number of multiple choice questions on the test, and

s represents the number of essay questions on the test.

m+s= 26

3m + 8s = 123

How many essay questions are on the test?

Answer:

2x - 15 +21 = -18

2x + 6 + 18 = 0

2x + 24 =0 ...it is a linear equation

if u want to solve for X then..

2x = -24

X = - 24

2

X = -12

Answer:

The correct answer is B

Step-by-step explanation:

First, do the first side which is 5w+8-w

5w+8-w

4w+8

Now the equation on the other side is 6w-2(w-4)

6w-2w+8

4w+8

Answer:

Unit rate = 2 mph

Step-by-step explanation:

Distance travelled = 1½ miles = \( \frac{3}{2} \) miles

Time taken = ¾ hours

\(Unit \: rate = \frac{distance \: travelled}{time \: taken} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ \frac{3}{2} }{ \frac{3}{4} }\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3}{2} \times \frac{4}{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \: mph (miles \: per \: hour)\)

Answer;

11

Step-by-step explanation:

2 X (3-1)

2 X 2= 4

44 divided by 4= 11

Step-by-step explanation:

Eueydhhdgdgdbdbddbdbhd

Answer:

Hello,

\(R=\dfrac{18}{\pi}\ (cm)\)

Step-by-step explanation:

\(Formula: \ L=\theta*R\\\)

\(R=\dfrac{6}{\dfrac{\pi}{3} } =\dfrac{6*3}{\pi} =\dfrac{18}{\pi}\ (cm)\)

The inverse of the given function is expressed as y =  ±√x + 38

Given the equation below expressed as:

y = x²  - 36

Replace y with x

x = y² - 38

Add 38 to both sides of the equation

x + 38 = y² - 38 + 38
y² = x + 38

Take the square root of both sides

√y² = ±√x + 38

y =  ±√x + 38

Hence the inverse of the given function is expressed as y =  ±√x + 38

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Answer:

B on edge 2022

Step-by-step explanation:

took the quiz

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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