Total time driving to and from beach: 12.3 hours; averaging 58 mph there, 65 mph returning home.
To find the total time Paul's family spent driving to and from the beach, we can calculate the time for each leg of the trip and then add them together.
1. Time taken for the trip to the beach:
[tex]\[ \text{Time}_1 = \frac{\text{Distance}_1}{\text{Speed}_1} \][/tex]
2. Time taken for the return trip:
[tex]\[ \text{Time}_2 = \frac{\text{Distance}_2}{\text{Speed}_2} \][/tex]
Given:
[tex]- Distance to the beach, \( \text{Distance}_1 = 377 \) miles\\- Speed to the beach, \( \text{Speed}_1 = 58 \) mph\\- Speed returning home, \( \text{Speed}_2 = 65 \) mph[/tex]
Let's calculate:
[tex]1. \[ \text{Time}_1 = \frac{377}{58} \][/tex]
[tex]2. \[ \text{Time}_2 = \frac{377}{65} \][/tex]
Now, let's compute:
[tex]\[ \text{Time}_1 = \frac{377}{58} \approx 6.5 \text{ hours} \]\[ \text{Time}_2 = \frac{377}{65} \approx 5.8 \text{ hours} \][/tex]
Finally, to find the total time spent driving to and from the beach, we add these times:
[tex]\[ \text{Total time} = \text{Time}_1 + \text{Time}_2 \]\[ \text{Total time} \approx 6.5 + 5.8 \]\[ \text{Total time} \approx 12.3 \text{ hours} \][/tex]
So, Paul's family spent approximately 12.3 hours driving to and from the beach.
Shalika bought a purse for $120. The tax rate is 9%.
What is the total amount Shalika paid?
Helpppppp please don’t have to explain or write a long paragraph just help me out and give me an answer pleaseeeee fasttttttt
a bag of concrate can be used to make a 5ft by 7ft porch.if you want to make a 20ft by 28ft,porch. how many bags of concreate do you need? the answer is not 4
area of 5 x 7 porch = 5*7 = 35 sq. ft.
area of 20 x 28 porch = 20 *28 = 560 sq. ft.
560 / 35 = 16
so 16 bags are needed
three pizza are shared equally among eight people. how much does each person get?
Choose the correct description of the graph of the compound inequality x - 1 alt= 12 or 2x alt= 30.
Answer:
.
Which of the following is not a way to represent the solution of the inequality 2(x + 1) alt= 20?
Step-by-step explanation:
Identify the inverse of the following statement. If x = 2, then x + 3 = 5.
a) If x + 3 = 5, then x = 2.
b) If x + 3 ≠ 5, then x ≠ 2.
c) If x ≠ 2, then x + 3 ≠mc011-4.jpg 5
d) x = 2 and x + 3 = 5.
Answer:
C
Step-by-step explanation:
The inverse of a statement "If p then q" is the statement "if ¬p then ¬q". In our case p is "x=2" and q is "x+3=5". Moreover, the negations of p and q are "[tex]x \neq 2[/tex]" and [tex]x+3 \neq 5[/tex] respectively. Then, the inverse of the original statement is
[tex]\text{if} \quad x\neq 2 \quad \text{then} \quad x+3 \neq 5[/tex]
Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many whit cars did Rafael count
yellow car = x
white cars = 9x ( 9 times as many white cars)
9x +x = 40
10x = 40
x = 40/10 =4
4 yellow cars
9*4 = 36 white cars
A rectangle is divided into 2 equivalent triangles.
If the area of the rectangle is 6 7/10 cm, what is the area of 1 of the triangle?
I REALLY NEED HELP
What is the slope of the line graph?
Enter your answer in the box
Answer: The slope of the line is [tex]-\frac{1}{3}[/tex].
Explanation:
From the given graph it is noticed that the line passing through many points.
The coordinates of three given points are (-6,6), (0,4) and (6,2).
If a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the slope of the lie is defined by,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The line passing through two points (0,4) and (6,2). So the slope of the line is,
[tex]m=\frac{2-4}{6-0}[/tex]
[tex]m=\frac{-2}{6}[/tex]
[tex]m=-\frac{1}{3}[/tex]
Therefore, the slope of the line is [tex]-\frac{1}{3}[/tex].
How many times can 27 go into 192
a farmer has 24 crates of plums ready to sell. each crate contains.208 plums. how many plums doesthe farmer have in all? use reasoning to explain how you can use estimating to check your answer.
Susan was making two types of soup. She had 1 pint 10 oz. of chicken noodle soup and 3 pints, 12 oz. of vegetable soup. How much soup did she have altogether?
Determine the x- and y-intercepts of the graph of y=− 1 2 x−4 .
Clea estimates that a glass contains 250.55 mL of water. The actual amount of water in the glass is 279.48 mL. To the nearest tenth of a percent, what is the percent error in Clea's estimate?
I need help with number 24. It says is it possible that Lauren answered more questions correctly on the second math test than Antoine did? Explain.
Calculating the probability of getting more than 75% of answers right with random guessing is unlikely to yield a count higher than 24 correct answers. Therefore it is improbable for Lauren to have answered more questions correctly than Antoine. However, without specific data on Lauren's and Antoine's test results, we cannot say with absolute certainty.
Explanation:To ascertain if Lauren could have answered more questions correctly on her second math test than Antoine, we need to understand the concept of probability. In this case, we want to find P(x > 24) which means we want to find out if getting more than 75 percent (or more than 24 correct answers) out of 32 questions is possible. That is, did Lauren score more than 24? However, the probability of getting more than 75 percent of the 32 questions correct when randomly guessing is practically zero. Mathematically, we express this as P(x > 24) = 0.
This suggests obtaining a score higher than 24 is very difficult, and therefore it's unlikely that Lauren answered more questions correctly than Antoine, especially if answering was based on random guessing. However, without specifics about Lauren's or Antoine's performance, we can't say definitively.
Learn more about Probability here:https://brainly.com/question/32117953
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In a survey 11 people was asked if there should be more school days of theese 6 people agreed yes. What percent of particpanits agreed with the proposal?
3 erasers cost $4.41
Witch equation will help determine the cost of 4 erasers
To determine the cost of 4 erasers, set up a proportion using the given information.
Explanation:To determine the cost of 4 erasers, we can set up a proportion using the given information. We know that 3 erasers cost $4.41, so we can write the equation:
3 erasers / $4.41 = 4 erasers / x
To solve for x, we can cross-multiply:
3 * x = 4 * $4.41
x = (4 * $4.41) / 3
Calculating this, we find that the cost of 4 erasers is $5.88. So, the equation that will help determine the cost of 4 erasers is 3 erasers / $4.41 = 4 erasers / $5.88.
The correct equation that represents this relationship and would help determine the cost of 4 erasers is:[tex]\[ \frac{4}{x} = \frac{3}{4.41} \][/tex]
The correct option is (A).
The image shows multiple choice options for equations that could be used to determine the cost of 4 erasers given that 3 erasers cost $4.41.
To find the cost of 4 erasers, we would want to set up a proportion where the number of erasers is directly proportional to the total cost. Given that 3 erasers cost $4.41, we can write this relationship as:
[tex]\[ \frac{\text{Number of erasers}}{\text{Cost}} = \frac{3}{4.41} \][/tex]
We want to find the cost for 4 erasers, so we can set up an equation with [tex]\( x \)[/tex] representing the unknown cost for 4 erasers:
[tex]\[ \frac{4}{x} = \frac{3}{4.41} \][/tex]
This equation can be solved to find \( x \), the cost for 4 erasers. We can cross multiply to solve for \( x \):
[tex]\[ 3 \times x = 4 \times 4.41 \][/tex]
[tex]\[ x = \frac{4 \times 4.41}{3} \][/tex]
Let's solve for[tex]\( x \)[/tex] to find the cost of 4 erasers.
The cost for 4 erasers, given that 3 erasers cost $4.41, would be $5.88.
The correct equation that represents this relationship and would help determine the cost of 4 erasers is:
[tex]\[ \frac{4}{x} = \frac{3}{4.41} \][/tex].
complete question given below:
At Algorithms Pizza they have the exponential pizza, which is a 24-inch cheese pizza that costs $17.50. Each topping for the pizza costs $2.35. If Connor ordered the exponential pizza and was charged $29.25, how many toppings were on his pizza? Justify your answer by using an algebraic equation to solve this problem step by step
Answer:
5 toppings.
Step-by-step explanation:
Let there were x toppings on the exponential pizza ordered by Connor.
Then charges for toppings = $2.35x
If the cheese pizza costs = $17.50
Total charges for the pizza = (17.5 + 2.35x)
Total cost of the cheese pizza with toppings = $29.25
Equation to find the number of toppings will be
29.25 = 17.5 + 2.35x
2.35x = 29.25 - 17.5
2.35x = 11.75
x = [tex]\frac{11.75}{2.35}[/tex]
x = 5
Therefore, number of toppings on the pizza will be 5.
Margaret uses 1 3/4 teaspoons of vanilla to make 12 cupcakes. She to wants make 30 cupcakes. how much vanilla will Margaret use?
Write an equation of a line that is perpendicular to y = ½ x + 3 and passes through the point (10, -5).
Question 4 options:
y = 2x – 15
y = - 2x + 15
y= -2x – 5
y = -1/2 x
Admission to the amusement park was $29.50 per person. If x represents the total cost for 3 tickets, which equation is true?
A. $29.50 + x = 3
B. 29.50*X=3
C. $29.50 + 3 = x
D. 29.50*3=x
Use a five-step plan to solve the following word problem. Show all five steps in your response:
Doug is twice Anne's age. Doug is 34 years old. How old is Anne?
Doug is twice Anne's age. Doug is 34 years old. How old is Anne?
A cookie recipe for three dozen Caramel peanut butter bars uses 14oz of caramel. How much caramel (to the nearest ounce) should be used to make 120 bars for a cookie exchange
To make 120 caramel peanut butter bars, using a recipe that calls for 14 ounces of caramel for 36 bars, one would need 47 ounces of caramel (rounded to the nearest ounce).
Explanation:Given that a cookie recipe for three dozen caramel peanut butter bars uses 14 ounces of caramel, we need to determine the amount of caramel needed to make 120 bars. Since three dozen bars are equal to 36 bars, we can find how many times the amount of bars in the recipe fits into the desired 120 bars count by dividing 120 by 36.
This gives us 120 / 36 = 3.33. Multiplying this factor by the amount of caramel used for 36 bars gives us the amount needed for 120 bars: 3.33 * 14 ounces = 46.62 ounces. Therefore, 47 ounces of caramel (rounding to the nearest ounce) should be used to make 120 bars for a cookie exchange.
A local gym charges a membership fee of $20 then a monthly fee of $15. Organize the data for the cost of gym membership for a year
A sauce recipe uses 4 cans of tomatoes in every 212 quarts.
How many cans of tomatoes are used in each quart of the sauce?
Answer: 1 3/5.
Step-by-step explanation: It's 2 1/2 not 212.
Suppose C and D represent two different school populations where C > D and C and D must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary. A: (C + D)2 B: 2(C + D) C: C2 + D2 D: C2 − D2
Answer:
A.
Step-by-step explanation:
We have that C>0, D>o and C > D. Now,
A. [tex](C+D)^2= C^2+2CD+D^2[/tex]
B. 2(C+D) = 2C+2D
C. [tex]C^2+D^2[/tex]
D. [tex]C^2-D^2[/tex]
We have that [tex]C^2+2CD+D^2> C^2+D^2[/tex] (beacuse on left we have adding one extra positive term) and also [tex]C^2+D^2> C^2-D^2[/tex] (adding two positive values is greater than subtract two positive values), then
[tex]C^2+2CD+D^2> C^2-D^2[/tex]
also, [tex]C^2+2CD+D^2> 2C+2D[/tex] (also because the middle term). Then, the largest term is [tex](C+D)^2= C^2+2CD+D^2[/tex].
There are 16 tables in the school lunch room each table can seat 22 students. How many students can be seated at lunch at one time?
Mary purchased 4 tires by mail order. She paid $63.40 per tire plus $6.80 per tire for shipping and handling. There is no sales tax, because the tires were purchased out of state. She also had to pay $7.56 per tire for mounting and balancing. At a local store, Mary's total for the 4 tires with mounting and balancing would be $368 plus 88% sales tax. How much did Mary save by purchasing the tires through the mail?
How do you solve this 4x - 2x -20x + x
Answer:
The value of the expression is [tex]-17x[/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]4x - 2x -20x + x[/tex]
To solve the above expression we need to add the like terms as shown.
[tex]4x+x - 2x -20x[/tex]
[tex]5x - 22x[/tex]
[tex]-17x[/tex]
Hence, the value of the expression is [tex]-17x[/tex].
Euler's formula, V – E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. How many faces does a polyhedron with 5 vertices and 8 edges have?