Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Two friends visited a taffy shop. Jon bought 4 kilograms of strawberry taffy and 1 kilogram of banana taffy for $23. Next, Charlotte bought 5 kilograms of strawberry taffy and 2 kilograms of banana taffy for $34. How much does the candy cost?

A kilogram of strawberry taffy costs $____, and a kilogram of banana taffy costs $____.

No triangles can be constructed with the given side lengths.

As, The triangle inequality is a mathematical theorem that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In other words, for a triangle with sides a, b, and c, where c is the longest side, the following inequality holds true:

a + b > c

Here, sides of triangle are 4cm, 5 cm and 9 cm.

So, 4 + 5 = 9

Thus, No triangles can be constructed with the given side lengths.

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Answer:

centimeters: 141

meters: 1.41

Step-by-step explanation:

1.16 m to cm is 116

116+25 = 141

25 cm to meters is 0.25

1.16+0.25 = 1.41

Answer:

3667 miles driven

Step-by-step explanation:

2132 + 1535 = 3667

The 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).

The given data points are:

97.1, 98.1, 98, 97.7, 97.4, 99.3, 96.8

Step 1: Calculate the sample mean (µ):

µ = (97.1 + 98.1 + 98 + 97.7 + 97.4 + 99.3 + 96.8) / 7 ≈ 97.914

sample standard deviation (s):

≈ 0.839

Step 3: Calculate the standard error (SE):

SE = s / sqrt(n)

≈ 0.839 / sqrt(7) ≈ 0.317

Step 4: Find the t-value for a 90% confidence interval with 6 degrees of freedom (n - 1 = 7 - 1 = 6).

Using a t-distribution table  we find that the t-value is approximately 1.943.

Step 5: Calculate the margin of error (ME):

ME = t-value * SE

≈ 1.943 * 0.317 ≈ 0.615

Step 6: Calculate the confidence interval:

Lower limit = µ - ME ≈ 97.914 - 0.615 ≈ 97.299

Upper limit = µ + ME ≈ 97.914 + 0.615 ≈ 98.529

So, the 90% confidence interval for the mean body temperature of adults in the town is approximately (97.299, 98.529).

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The surface area of a figure is obtained as the sum of the areas of all the parts that compose a figure.

The figure for this problem is composed as follows:

Considering the total surface area of 160 ft², the area of each missing face is given as follows:

2 x (24 + 8 + A) = 160

64 + 2A = 160

2A = 96

A = 48 ft².

Considering a rectangle with dimensions 12 ft and x, with area of 48 ft², the length of the missing edge is given as follows:

12x = 48

x = 4 ft.

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Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

Answer:

x = 7

Step-by-step explanation:

Product of powers rule:

[tex] a^m \times a^n = a^{m + n} [/tex]

When you multiply two powers with the same base, add the exponents.

[tex] 3^5 \times 3^2 = 3^x [/tex]

Apply the rule above to the left side.

[tex] 3^{5 + 2} = 3^x [/tex]

[tex] 3^7 = 3^x [/tex]

[tex] x = 7 [/tex]

The total purchase is  $18.90.

We have,

A discount would reduce the cost of the purchase. A tax increases the cost of the purchase.

The first step is to determine the total cost of the items purchased.

Total cost = (cost of lb of cheese x lb bought) + (cost of sliced ham x lbs bought) + (cost of bread x loaves bought) + (cost of a bag of potato chips x number of bags bought) + (cost of one salsa container x number of containers bought)

(1.99 x 1/2) + (3 x 3.29) + (1.59 x 2) + (2 x $3) + (1.39 x 1) = $20.39

Since, the total cost is greater than $20 she qualifies for the 10% discount

Total cost after the discount = (1 - 0.1) x $20.39

0.9 x $20.39= $18.35

Cost after the tax = (1 + 0.03) x $18.35

1.03 x $18.35 = $18.90

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complete question:

You have several purchases you need to purchase 1/2 lb of cheese, 3lbs sliced ham, 2 loaves of bread, 4 bags of potato chips, and 1 container of salsa. You have a coupon for $4.00 off of your purchase totals more than $15.00 or %10 off if the total is more than $20.00. The food sales tax is 3%. What is your total purchase?

Cheese:$1.99/lb

Sliced ham:$3.29/lb

Bread:$1.59/loaf

Potato chips:$1.99/ea Or 2 for $3.00

Salsa:$1.39/container

Be sure to include in your response.

The steps you followed to complete your computations.

The choice you made regarding which discount to use.

The total cost of your purchase.

Answer:

Step-by-step explanation:

The 40 degree angle we are given is called an angle of depression. Because of geometry and the fact that the base of the triangle and this dotted line are parallel to one another, the base angle inside the triangle is also 40. These are called alternate interior angles. The x represents the hypotenuse of the triangle. We can use right triangle trig to find it. The side measuring 500 is OPPOSITE the reference angle of 40 and the missing side is the HYPOTENUSE, so the trig ratio we will use is sin which is, according to SohCahToa, opposite side over hypotenuse; namely:

[tex]sin40=\frac{500}{x}[/tex]

Algebraically, we will multiply both sides by x and then divide by sin40 to get:

[tex]x=\frac{500}{sin40}[/tex]

Make sure your calculator is in degree mode and not radian mode and enter the problem as you see it above to get that

x = 777.9m, choice A.

[tex]-29~~,~~\stackrel{-29+7}{-22}~~,~~\stackrel{-22+7}{-15}~~,~~...\hspace{5em}\stackrel{\textit{common difference}}{d=+7} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-29\\ n=92\\ d=7 \end{cases} \\\\\\ a_{92}=-29+(92-1)7\implies a_{92}=-29+637\implies \boxed{a_{92}=608}[/tex]

The entire number is odd.

For any number n, the predecessor is n - 1 and the successor is n + 1.

We have,

To find the place value of the number in the thousand's place for the number obtained by adding 60 tens, 58 hundreds, and 685 ones, we can start by realizing that 60 tens are the same as 600, and 58 hundreds are the same as 5800.

Therefore, we have:

600 + 5800 + 685 = 7085

So the number is 7085.

The digit in the thousand's place is 0 since there is no digit in the thousand's place.

Therefore, the place value of the number in the thousand's place is 0.

To determine if the number is even or odd, we can look at the unit digit, which is 5.

Since 5 is an odd number,

The entire number is odd.

2.

The predecessor of a number is the number that comes before it, and the successor of a number is the number that comes after it.

To find the predecessor of a number, we subtract 1 from the number, and to find the successor, we add 1 to the number.

For example,

Let's say we want to find the predecessor and successor of the number 7.

The predecessor of 7 is 6, since 7 - 1 = 6.

The successor of 7 is 8, since 7 + 1 = 8.

In general,

For any number n, the predecessor is n - 1 and the successor is n + 1.

Thus,

The entire number is odd.

For any number n, the predecessor is n - 1 and the successor is n + 1.

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The 95% confidence interval for the population mean is (47.00, 48.90).

A sample of size n=78 is drawn from a normal population with a standard deviation of σ=5.1. The sample mean is x=47.95.

Using this information, we can estimate the population mean using the formula:

μ = x ± z*(σ/√n)

where μ is the population mean, x is the sample mean, z is the z-score for the desired level of confidence (e.g., 1.96 for a 95% confidence interval), σ is the population standard deviation, and n is the sample size.

Assuming a 95% confidence level, the z-score is 1.96. Plugging in the given values, we get:

μ = 47.95 ± 1.96*(5.1/√78)

Solving for the upper and lower bounds of the confidence interval, we get:

μ = 47.95 ± 0.95

So the 95% confidence interval for the population mean is (47.00, 48.90). This means that if we were to repeat this sampling process many times, we would expect the true population mean to fall within this interval 95% of the time.

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x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Angle L's in the triangle LMN is,

⇒ L = 72.54°

We have to given that;

A triangle LMN is shown in figure.

And, The sides are,

Since, We know that;

A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Since, We know that;

⇒ sin L = Opposite / Hypotenuse

And, cos L = Base / Hypotenuse

Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, We can use trigonometry formula to find the value of angle l we get;

⇒ sin L = Opposite / Hypotenuse

⇒ sin L = LM / LN

⇒ sin L = 18/60

Taking arc sin both side, we get;

⇒ L = 72.54°

Therefore, The value of measure of angle L is triangle LMN is,

⇒ L = 72.54°

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Figure ABCD is translated 3 units right and 1 unit up.

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Based on the information provided, we have the follwoing:

(x, y)                               →                  (x + h, y + k)

A (2, 3)                              →                  A' (5, 4).

5 = 2 + h

h = 5 - 2

h = 3 (3 units right).

4 = 3 + k

k = 4 - 3

k = -3 (1 unit up).

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Complete Question:

Describe the translation of figure ABCD. Complete the sentence to explain your answer.

Figure ABCD is translated  unit(s) right and  unit(s) up.

a) Bonita Company's income from operations is $145,070.

b) Bonita Company's net income is $163,430.

c) the comprehensive income for Bonita Company is $173,310.

d) Since, we are not given the beginning balance of retained earnings, we cannot calculate the exact retained earnings balance at December 31, 2025.

Given that;

Presented below is information related to Bonita Company at December 31, 2025, the end of its first year of operations.

Sales revenue : 335,550

Cost of goods sold : 135,580

Selling and administrative expenses : 54,900

Gain on sale of plant assets: 30,790

Unrealized gain on available-for-sale debt investments: 9,880

Interest expense: 6,050

Loss on discontinued operations: 12,200

Dividends declared and paid: 5,060

(a) The cost of items sold, selling, and administrative expenses must be subtracted from the revenue from sales in order to determine the income from operations.

Revenue from operations is equal to sales revenue minus the cost of the goods sold plus selling and administrative costs.

Operations profit = $335,550 - $135,580 - $54,900 $145,070

was earned through operations.

As a result, Bonita Company's income from operations is $145,070.

(b) We must add or deduct all gains, losses, and expenses from the income from operations in order to determine the net income.

Net income is calculated as follows:

Income from operations - Loss on ceased operations - Gain on sale of plant assets - Unrealized gain on debt investments that are available for sale Net income equal

$145,070 + $30,790 + $9,880 + $6,050 + $12,200 - $5,060.

$163,430 in profit

As a result, Bonita Company's net income is $163,430.

(c) To determine the comprehensive income, we need to add or subtract all gains, losses, and expenses that are not included in net income. In this case, the only item that needs to be added is the unrealized gain on available-for-sale debt investments.

Comprehensive income = Net income + Unrealized gain on available-for-sale debt investments Comprehensive income

= $163,430 + $9,880

Comprehensive income = $173,310

Therefore, the comprehensive income for Bonita Company is $173,310.

(d) To calculate the retained earnings balance, we need to start with the beginning balance of retained earnings (which is not given in this problem) and add the net income, then subtract any dividends declared and paid.

Retained earnings balance = Beginning balance of retained earnings + Net income - Dividends declared and paid Retained earnings balance

= Beginning balance of retained earnings + $163,430 - $5,060

Retained earnings balance = Beginning balance of retained earnings + $158,370

Since, we are not given the beginning balance of retained earnings, we cannot calculate the exact retained earnings balance at December 31, 2025.

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The expression, in the end, is 10 x 3 = 30

i.e

Length = 10

Width = 3

The number of tiles = 10 x 3 = 30

We have,

We see that,

The number of tiles:

18, 24, 30,

This is an arithmetic sequence.

So,

The next term:

= 30 + 6

= 36

Now,

The length is a sequence in ascending order of the factor of the arithmetic sequence.

So,

30 is a factor of 2, 3, 5, 6, and 10.

This means,

The expression, in the end, is 10 x 3 = 30

So,

Length = 10

Width = 3

The number of tiles = 10 x 3 = 30

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Answer:

0.4

Step-by-step explanation:

Let A be the event of selecting a bead with two holes and B be the event of selecting a red bead. We are given P(A) = 0.5 and P(A and B) = 0.2. We need to find P(B|A), the probability of selecting a red bead given the bead has two holes.

By definition of conditional probability, we have:

P(B|A) = P(A and B) / P(A)

Substituting the given values, we get:

P(B|A) = 0.2 / 0.5

Simplifying, we get:

P(B|A) = 0.4

Therefore, the probability of selecting a red bead given the bead has two holes is 0.4.

Answer: 0.2.

Step-by-step explanation:

Line segment PT ≅ line segment PT by the reflexive property.

ΔPRT ≅ ΔTVP by the SSS triangle congruence theorem

The SSS congruence theorem (side-side-side congruence theorem) states that if all three sides of one triangle are congruent to the corresponding three sides of another triangle, then both are considered congruent triangles.

According to the reflexive property, a line or angle is equal to itself, therefore, Line segment PT ≅ line segment PT by the reflexive property.

This also implies that both triangles have three pairs of corresponding sides that  congruent, therefore, ΔPRT ≅ ΔTVP.

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The probability that Jess will win only the third game out of three games is 0.144, or 14.4%

To calculate the probability that Jess will win only the third game out of three games, we will use the concept of independent events. In this scenario, we have the following events:

1. Jess loses the first game.
2. Jess loses the second game.
3. Jess wins the third game.

Since the events are independent, we can calculate the probability of this specific sequence occurring by multiplying the probabilities of each individual event:

1. Probability of losing the first game: 1 - 0.4 = 0.6
2. Probability of losing the second game: 1 - 0.4 = 0.6
3. Probability of winning the third game: 0.4

Now, we multiply these probabilities together:

0.6 * 0.6 * 0.4 = 0.144

So, the probability that Jess will win only the third game out of three games is approximately 0.144, or 14.4% when rounded to three decimal places.

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Answer:

b) Answers may vary, e.g., I would determine the x- and y-intercepts because I think it's easier. Lesson 1.1, page 12. 1. a) on the graph because if b) not on ...64 pages

Step-by-step explanation:

Determine the x and y intercept for each of the equations. Write your answer as a coordinate pair. If it does not have an intercept, explain your reasoning.

The inverse function of f(x) is given as follows:

[tex]f^{-1}(x) = \sqrt{x}[/tex]

The function f(x) graphed in this problem is given as follows:

f(x) = x².

Using the notation y = f(x), we have that:

y = x².

To obtain the inverse, first we exchange y and x, hence:

x = y².

Finally, we must isolate the variable y, hence:

[tex]y = \pm \sqrt{x}[/tex]

[tex]y = \sqrt{x}[/tex] -> we take only the positive and the domain is the non-negative numbers.

Hence the inverse function is:

[tex]f^{-1}(x) = \sqrt{x}[/tex]

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Answer:

50 employees can the company send to the conference

Step-by-step explanation:

2500:50= 50

Answer:

cioè x ≥ 1; si avrà pertanto x > 0

Step-by-step explanation:

EXERCISE 2. Risolvere le seguenti disuguaglianze:

(1) | x−1 |< 3

(2) | x+1 |> 2

(3) | 2x+1 |< 1

(4) | x−1 |<| x+1 |

Caso: (a): | x−1 |< 3, risolvo

x−1 < 3

x ≥ 1

∪

−x+1 < 3

x < 1

, si avrà quindi

x < 4

x ≥ 1

cioè 1 ≤ x < 4 e

x > −2

x < 1

cioè −2 < x < 1. L’unione tra le due dà la soluzione −2 < x < 4

Caso: (b):

x+1 > 2

x ≥ −1

∪

−x−1 > 2

x < −1

, si avrà quindi

x > 1

x ≥ −1

cioè x > 1 e

x < −3

x < −1

cioè x < −3,

pertanto x < −3 ∪ x > 1

Caso: (c):

2x+1 < 1

x ≥ −1

2

∪

−2x−1 < 1

x < −

1

2

, si avrà quindi

x < 0

x ≥ −1

2

cioè −

1

2 ≤ x < 0 e

x > −1

x < −

1

2

cioè

−1 < x < −

1

2

. pertanto −1 < x < 0

Caso: (d): in questo caso,

−x+1 < −x−1

x < −1

∪

−x+1 < x+1

−1 ≤ x < 1

∪

x−1 < x+1

x ≥ 1

, si avrà quindi

0 < −2

x < 1

cioè non si hanno soluzioni e

x > 0

−1 ≤ x < 1

cioè 0 < x < 1 e

0 < 2

x ≥ 1

cioè x ≥ 1; si avrà pertanto x > 0

Answer:

The mean distance to his friends' house is between 2 -3 blocks.

Step-by-step explanation:

1. Mean = Average.

Average = (n1+n2+n3....nx)/x

2. The average = 1+2+5+3+2+2+5+3/8

3. Therefore, the answer is 2.875, making the mean between 2 and 3

Answer:

The statement that supports the data is the mean distance to his friends' houses is in between 2 and 3 blocks.

Step-by-step explanation:

What is mean, median and mode?

Mean: The average of the given data points.

Median: The central point of the whole data set.

Mode: The number that occurs for the maximum times in the data set.

Given:

Karl records the number of city blocks from his house to each of his friends houses.

Data set for the number of city blocks to eight friends houses:

{1, 2, 5, 3, 2, 2, 5, 3}

The first option: it is given that the maximum number of blocks the Karl lives from his friend is 4, but according to the data set, the maximum number of house blocks should be 5.

Hence, this option is incorrect.

The second option: It is given that the mode shows that Karl has 3 friends who live 3 blocks from him, but according to the given data set Karl has 3 friends who lives 2 blocks from him. Hence the mode is 2.

Hence, this option is incorrect.

The third option: It is given that the minimum distance from Karl's house to a friend's is 2 blocks, but according to the given data set the minimum distance from Karl's house to a friend's is 1 block.

Hence, this option is incorrect.

The fourth option:  It is given that the mean distance to his friend's houses is in between 2 and 3 blocks.

We will find the mean for the given data set.

⇒ Mean = (Sum of all the data points) / (Total number of data points)

⇒ Mean = (1 + 2 + 5 + 3 + 2 + 2 + 5 + 3)/8

⇒ Mean = 23/8

⇒ Mean = 2.875

∴ The mean distance from Karl to his friend's houses is 2.875 which is in between 2 and 3.

Hence, this option is correct.

Therefore, the fourth option which says the mean distance between Karl and his friend's houses is in between 2 and 3 is correct.

Answer:

Let B be the number of balls Brandon had initially, and C be the number of balls Cody had initially.

We know that Brandon had 40% more balls than Cody, so:

B = 1.4C

We also know that Brandon gave 30% of his balls to Cody, so Cody received:

0.3B

And we know that Cody gave 50% of his balls to Brandon, so Brandon received:

0.5(0.3B) = 0.15B

Now, we can set up an equation to represent the final number of balls Cody had:

C + 0.3B - 0.5(0.3B) = C - 0.15B

And we know from the problem that Cody had 852 less balls than Brandon in the end, so:

C - 0.15B = B - 852

We can substitute B = 1.4C into this equation to get:

C - 0.15(1.4C) = 1.4C - 852

Simplifying this equation, we get:

0.79C = 852

Solving for C, we get:

C = 1078

And since B = 1.4C, we have:

B = 1.4(1078) = 1511.2

So Brandon initially had 1511 balls. However, since we're dealing with whole numbers of balls, we need to round to the nearest integer. Therefore, the final answer is:

Brandon initially had 1511 balls

Step-by-step explanation:

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