A cannery processed 1,445 pounds of strawberries in 4.5 hours. The cannery processed 2,320 of strawberries in 7 hours. Write a linear equation to model the relationship between the weight of strawberries S and time T. How many pounds of strawberries can be processed in 11 hours?

Arc DB measure less than 180 degrees,  is called a minor arc.

Option (b) is correct

A minor arc is an arc whose angle is less than 180 degrees.

From given figure, It is observed that, arc DB measure less than 180 degrees is called a minor arc.

Hence, option (b) is correct.

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Answer:

for online school people it will be 2,3,4

Step-by-step explanation:

i did the assigment

Final answer:

The provided algebraic expression 4m+6p-8mp cannot be solved or simplified further without additional context, such as specific values for m and p or instructions for solving for one variable in terms of the other.

Explanation:

The original question, "how to solve 4m+6p-8mp", seems to be a request for simplification or to apply given values to an algebraic expression. Without specific values or instructions to solve for one of the variables, the expression cannot be "solved" in the conventional sense of finding a numerical answer. However, we can explore quick ways to simplify or rearrange such an expression if additional context or information were provided, such as values for m and p or instructions on solving for one variable in terms of the other.

In the given two column proof two sides and included angles are equal.

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles .In the figure sides BD≅BD , AB≅ BC and <ABD ≅,BDD Therefore triangle ABD and triangle CBD are congruent by SAS property of congruence.

The correct  option for missing statement is D. ΔABD ≅ ΔCBD .

Answer:

ΔABD ≅ ΔCBD

Step-by-step explanation:

Guys this is the right answer,  ΔABD ≅ ΔCBD. I got it right on my test!

Final answer:

The absolute value equation that represents the minimum and maximum heights of adult women, with heights represented by x, is |x - 58| = 34.

Explanation:

To write an absolute value equation representing the minimum and maximum heights of adult women, where the shortest known adult woman is about 24 inches tall and the tallest known adult woman is about 92 inches tall, we can use the variable x to represent an adult woman's height. The midpoint between the smallest and largest height is (24 + 92) / 2 = 58 inches. The distance from this midpoint to each extreme is 34 inches, because 92 - 58 = 34 and 58 - 24 = 34. So, the absolute value equation would be |x - 58| = 34. This equation represents that the height of an adult woman can deviate from 58 inches by 34 inches to be either at the minimum or maximum height recorded.

Final answer:

The absolute value equation representing the minimum and maximum heights of adult women is |x - 58| = 34, where x is the height in inches.

Explanation:

The objective is to write an absolute value equation to represent the minimum and maximum heights of adults.

Using the heights given for the shortest and tallest known adult women, 24 inches and 92 inches respectively, we set the variable x to represent an unknown height.

To express this as an absolute value equation, we identify the midpoint between these two heights, which is (24 inches + 92 inches) / 2 = 58 inches.

The distance from the midpoint to either extreme is (92 inches - 58 inches) = 34 inches, which is the absolute difference.

Therefore, our absolute value equation is |x - 58| = 34.

This equation tells us that the height x must be either 34 inches above or below 58 inches, which corresponds to the minimum and maximum heights of 24 inches (58 - 34) and 92 inches (58 + 34) respectively.

The number of sodas sold is 145, and the number of hot dogs sold is 112. (145 sodas, 112 hot dogs)

Let's denote:

-  s  as the number of sodas sold.

- h  as the number of hot dogs sold.

Given that the total number of sodas sold is 145, we have:

[tex]\[ s = 145 \][/tex]

And we know that the number of hot dogs sold is 33 less than the number of sodas sold:

[tex]\[ h = s - 33 \][/tex]

Now, substitute the value of  s  into the equation for h :

[tex]\[ h = 145 - 33 \]\[ h = 112 \][/tex]

So, the number of hot dogs sold is 112, and the number of sodas sold is 145.

Answer:

C.

Step-by-step explanation:

x4 + 2x2 + 2 has no real roots

The additional information needed to prove that ΔABC ≅ ΔDEF by ASA is two pairs of congruent angles and the included side between the two pairs of congruent angles.

We are given that;

The two triangles ΔABC and ΔDEF

Now,

To prove that ΔABC ≅ ΔDEF by ASA (Angle-Side-Angle) congruence criterion, we need the following information:

Two pairs of congruent angles.

The included side between the two pairs of congruent angles.

If two angles and one side of one triangle are equal to two angles and one side of another triangle, then they are congruent. For example, in ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and BC= EF then ΔABC ≅ ΔDEF by AAS criteria

Therefore, by congruent triangles answer will be two pairs of congruent angles and the included side between the two pairs of congruent angles.

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Answer:

The probability that two randomly selected tulip bulbs are both red is 0.11

The probability that the first bulb selected is red and the second is yellow is 0.13

The probability that the first bulb selected is yellow and the second is red is 0.13                

Step-by-step explanation:

A bag of 29 tulip bulbs contains:

10 red tulip bulbs

11 yellow tulip bulbs

8 purple tulip bulbs

Part 1:What is the probability that two randomly selected tulip bulbs are both red?

No. of red tulips = 10

So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]

                                                                             = [tex]\frac{10}{29}[/tex]

Since 1 bulb is drawn . So, total no. of bulbs remaining = 28

And that 1 bulb is drawn from red bulbs . So, remaining red bulbs = 9

So, probability of getting red bulb in second draw = [tex]\frac{9}{28}[/tex]

Thus the probability that two randomly selected tulip bulbs are both red:

= [tex]\frac{10}{29}\times\frac{9}{28}[/tex]

= [tex]\frac{45}{406}[/tex]

= [tex]0.11[/tex]

Hence  the probability that two randomly selected tulip bulbs are both red is 0.11

Part 2: What is the probability that the first bulb selected is red and the second is yellow?

No. of red tulips = 10

So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]

                                                                             = [tex]\frac{10}{29}[/tex]

Since 1 bulb is drawn . So, total no. of bulbs remaining = 28

No. yellow bulbs =11

So, probability of getting yellow bulb in second draw = [tex]\frac{11}{28}[/tex]

Thus the probability that the first bulb selected is red and the second is yellow

= [tex]\frac{10}{29}\times\frac{11}{28}[/tex]

= [tex]\frac{55}{406}[/tex]

= [tex]0.13[/tex]

Hence the probability that the first bulb selected is red and the second is yellow is 0.13

Part 3: What is the probability that the first bulb selected is yellow and the second is red?

No. of yellow tulips = 11

So, probability of getting yellow tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]

                                                                             = [tex]\frac{11}{29}[/tex]

Since 1 bulb is drawn . So, total no. of bulbs remaining = 28

No. red bulbs =10

So, probability of getting red bulb in second draw = [tex]\frac{10}{28}[/tex]

Thus the probability that the first bulb selected is red and the second is yellow

= [tex]\frac{11}{29}\times\frac{10}{28}[/tex]

= [tex]\frac{55}{406}[/tex]

= [tex]0.13[/tex]                          

Hence the probability that the first bulb selected is yellow and the second is red is 0.13                                        

The cost that's necessary to pay the loan will be $31,616.16.

First, we need to calculate the effective monthly interest rate. This will be:

i = 0.053/12

= 0.0044

The effective annual interest rate will then be:

i = (1 + 0.0044)^12 - 1

I = 0.0543

Next thing will be to calculate the present worth of all the loans which will be:

P = 6125 + 6125 (1 + 0.0543) + 6125 (1 + 0.0543)² + 6125(1 + 0.0543)³

P = $22,671.40

The worth of the loans after four years will be:

P = 22671.40 (1 + 0.0543)⁴

= $31,616.16

In conclusion, the correct option is $31,616.16.

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To calculate the total cost of Toby's 4 Stafford loans, the monthly amount for one loan is first calculated and then multiplied by four and by the number of months. The correct total lifetime cost is approximately $31,569.60.

To determine the total lifetime cost that Toby will pay to pay off his 4 Stafford loans, each with a principal of $6,125, an interest rate of 5.3% compounded monthly, and a loan duration of ten years, we need to calculate the monthly payment for a single loan and then multiply by the number of loans and the duration. The formula for the monthly payment on an installment loan is:

P = P[r(1+r)^n] / [(1+r)^n - 1]

where:

Using the data given:

P = $6,125 * [0.004417(1 + 0.004417)^120] / [(1 + 0.004417)^120 - 1]

Calculating this gives us a monthly payment of approximately $65.77 for each loan. Toby took out 4 loans, so his total monthly payment is 4 * $65.77 = $263.08.

The total lifetime cost for a single loan is the monthly payment * number of payments (120), which is:

Total cost for one loan = $65.77 * 120 = $7,892.40

And the total lifetime cost to pay off all 4 loans:

Total cost for all loans = $7,892.40 * 4 ≈ $31,569.60

Therefore, rounding each loan's payment to the nearest cent, the total lifetime cost to pay off all 4 of Toby's loans is roughly $31,569.60, making the answer option b the correct one.

Answer:

C. Postulate.

Step-by-step explanation:

We are asked to find the term that defines the given statement.

Theorem: We know that a theorem is proved by a chain of reasoning. Ir is not self evident.

Definition: We know that definition is a statement of the exact meaning of a word.

Postulate: We know that a postulate is a statement that is taken to be true without any proofs, therefore, postulate is the correct choice.

The solution of equation 9x + 7 = 7x - 5 is -6.

The equation 9x + 7 = 7x - 5 can be solved by first isolating x on one side. To do this, we subtract 7x from both sides of the equation, which gives us 2x + 7 = -5. Next, we subtract 7 from both sides to get 2x = -12. Finally, we divide both sides by 2 to find that x = -6. This single solution can be checked by substituting x back into the original equation to verify that both sides equal out, confirming it is an identity. Therefore, the correct solution is x=-6.

To validate the result, we substitute -6 back into the original equation:
9(-6) + 7 = 7(-6) - 5
-54 + 7 = -42 - 5
-47 = -47, which is indeed an identity.