Final answer:
The inequality to represent the number of days, d, Kyle can rent equipment with $121 is 25 + 13d ≤ 121. After solving, the result is d ≤ 7, meaning Kyle can rent the equipment for at most 7 days.
Explanation:
To represent the number of days, d, that Kyle can rent equipment given he has $121, we set up an inequality taking into account the flat rate and the daily insurance cost. The equipment rental company charges a flat rate of $25 plus $13 per day for insurance. Therefore, the cost for d days would be $25 + $13d. Since Kyle has $121, we can write the inequality as:
25 + 13d ≤ 121.
This inequality shows that the total cost of renting the equipment for d days, which includes the flat rate and the per-day insurance cost, must be less than or equal to the amount Kyle has.
To solve for d, subtract 25 from both sides:
13d ≤ 121 - 25
13d ≤ 96
Now, divide both sides by 13 to find the maximum number of days Kyle can rent the equipment:
d ≤ 96 / 13
d ≤ 7
Thus, Kyle can rent the equipment for at most 7 days.
Kyle can rent equipment for at most 7 days with $121, considering a flat rate of $25 and a $13 per day insurance charge, as represented by the inequality 25 + 13d ≤ 121.
Explanation:To find the inequality that represents the number of days, d, for which Kyle can rent equipment given that he has $121, we need to consider both the flat rate and the per day insurance charge.
The flat rate for renting equipment is $25, and the daily insurance charge is $13 per day. So, the cost for d days would be the flat rate plus the daily charge times the number of days, which can be represented by the following equation:
Cost = Flat rate + (Insurance charge per day × Number of days)
Cost = 25 + 13d
Since Kyle only has $121, he can spend up to that amount. Therefore, the inequality would be:
25 + 13d ≤ 121
To solve for d:
13d ≤ 121 - 25
13d ≤ 96
d ≤ 96/13
≤ 7.38
Since Kyle can't rent equipment for a fraction of a day, we take the whole number part of the division result. This means that Kyle can rent the equipment for at most 7 days.
The range of F(x) = 6 * 3x is all positive real numbers.
Given a circle with a diameter of 4, which equation expresses π as the ratio of the circumference of a circle to its diameter?
C /4 = π
Took the test myself, this is the answer.
Brent was looking at his cell phone bill and saw that the total number of texts he has sent is tracked, as shown below:
Month
Texts
1
120
2
237
3
354
4
471
The function representing Brent's texting per month is f(m) = 117m + 3. What does the 117 represent?
It should be the additional texts per month or D
Answer:
The number of texts he sends per month
Step-by-step explanation:
The function f(m) = 117m + 3 is a linear function, which is in the form f(x) = mx+b. In this form, m (the number beside our variable) is the slope, or rate of change, and b (the number added or subtracted) is the y-intercept.
In our function, 117 is the number beside the variable, which makes it the slope. This is the rate of change of this function; it describes how the dependent variable (number of texts) changes for every change in the independent variable (months).
In other words, it tells how many texts he sends per month.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number?
The answer is 0.5.
To find the answer, understand the place value system in numbers.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number.
To find the answer, we need to understand the place value system. In the number 653,841, the digit in the hundreds place is 8, and the digit in the thousands place is 5. Therefore, 1/10 of the digit in the thousands place is 0.5.
So, the answer is 0.5.
Box i contains 4 red and 8 blue marbles while box ii contains 5 red and 3 blue marbles. an unfair coin is tossed –whose probability of turning up heads is 40%. if the coin comes up heads box i is chosen and a random marble is chosen, otherwise if it is tails the marble is chosen from box ii.(a)find the probability a red marble is chosen.(b)if a red marble is chosen, what is the probability it came from box i? (c)if a blue marble is chosen, what is the probability it came from box i?
Write the epxressions for the equivalent capacitance of two capacitors write your answers in terms of c1 and c2
in fifteen minutes greg sailboat went 3/6 miles, gina sailboat went 6/6 miles, and stuart sailboat went 4/6 miles. whose sailboat went the longest distance in fifteen minutes?
find the domain of
[tex]f(x) = \frac{ \sqrt{x + 2} }{ {x}^{2} - 25 } [/tex]
A pendulum travels 30 inches on its first swing. During each of its subsequent swings, it travels 90 percent of the previous swing.
Answer:
a1= 30 and r=0.9
Step-by-step explanation:
edge
Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
a) The height of the red prism is one-third the height of the blue prism.
b) The height of the red prism is the same as the height of the blue prism.
c) The height of the red prism is six times the height of the blue prism.
d) The height of the red prism is three times the height of the blue prism.
Answer:
D
Step-by-step explanation:
Jack purchased a box of 1,000 candy guitar lollipops to sell in the bakery for $20.00. How much did he pay for each lollipop?
Which multiplication expression that does not belong based on scaling. Explain.
Choose an expression
6 x 2 1/2
6 x 3 3/5
1/2 x 6
2 2/5 x 6
Cream filled chocolates are $3.59 a pound Billy bought 1/2 pound of vanilla creams what was the cost round your answer
Cheryl paid $3.00 for a pair of socks and eight times as much for a pair of shoes. Her brother Kevin also bought socks and shoes but paid twice as much as Cheryl did for each. How much money did they spend together ?
8pints compared to 15 cups
if c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE
Answer:
[tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Step-by-step explanation:
As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.
Remember that a bisector is a line that equally divides an angle.
So,
[tex]\angle AMC = \angle DMC\\3x+6=8x-49[/tex]
Solving for [tex]x[/tex], we have
[tex]6+49=8x-3x\\5x=55\\x=11[/tex]
Then, we substitute this value in each expression to find the angles.
[tex]\angle AMC = 3x+6 = 3(11)+6=33+6=39[/tex]
[tex]\angle DMC = 8(11)-49=88-49=39[/tex]
Therefore, the measures of those angles are [tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Find the fifth term of A n = 2n
Jeannie's restaurant served 58 customers on Monday. After the first day the amount of customers served decreases at a rate of 2.5% each day.
What is the explicit rule for this situation and approximately how many customers will be served on the 6th day?
Round to the nearest customer.
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of customers on the 6th day.
A n = 58 x (0.975) n - 1, A n = 58 x (0.025) n - 1, A n = 58 (1.025) n - 1, 51, 49, 48, 46,
Answer:
51 customers
Step-by-step explanation:
Jeannie's restaurant served 58 customers on Monday.
Rate of decrement r =2.5 % = 0.025
Formula : [tex]y=a(1-r)^{n-1}[/tex]
A is the initial amount
r is the rate
n is the no. of days
So, Substitute the values
[tex]y=58(1-0.025)^{n-1}[/tex]
[tex]y=58(0.975)^{n-1}[/tex]
So, explicit rule : [tex]A_n=58(0.975)^{n-1][/tex]
Now to find the no. of customers will be served on the 6th day
Substitute n = 6
[tex]A_6=58(0.975)^{6-1}[/tex]
[tex]A_6=51.1035[/tex]
So, 51 customers will be served on the 6th day
y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.
Answer:
2
0
two real solutions
Step-by-step explanation:
from edge!!
To find the x-intercepts of the quadratic equation representing the height of a dolphin's jump, we can use the quadratic formula by plugging in the coefficients from the equation y = -16x^2 + 32x - 10. The intercepts indicate the times when the dolphin's height above water is zero feet.
Explanation:The question involves finding the x-intercepts of a quadratic equation, which represent the points where a parabola crosses the x-axis. In this context, the x-intercepts correspond to the times when the dolphin's height above water is 0 feet. To find the x-intercepts, we can use the quadratic formula:
x = −b ± √(b² − 4ac) / (2a)
For the equation y = −16x² + 32x − 10, the coefficients are a = −16, b = 32, and c = −10. By substituting these values into the quadratic formula, we can calculate the times when the dolphin is at the water level (y=0). Since this is a mathematical problem involving a real-world scenario, it is essential to check that the resulting times make sense within the context. Negative values for time, for example, would not be physically meaningful.
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Use the diagram of the right triangle above and round your answer to the nearest hundredth. If m
Answer choices:
A) 17.32 m
B) 6.83 m
C) 14 m
D) 9.99 m
Answer:
b. 6.93 m.
Step-by-step explanation:
We have been given triangle ABC and we are asked to find the measure of a.
We will use law of sines to solve our given problem.
[tex]\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are opposite sides of angle A, B and C respectively.
First of all, we will find the measure of angle B using angle sum property.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]30^{\circ}+\angle B+90^{\circ}=180^{\circ}[/tex]
[tex]\angle B+120^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-120^{\circ}[/tex]
[tex]\angle B=60^{\circ}[/tex]
Upon substituting our given values in law of sines we will get,
[tex]\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}[/tex]
[tex]\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}[/tex]
[tex]\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5[/tex]
[tex]a=\frac{12}{\sqrt{3}}[/tex]
[tex]a=6.9282032302755\approx 6.93[/tex]
Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.
Describe the test grades using the measures of center
In a line of students ,Jenna is number 8.The teacher says the rule for a number pattern is add4.The first term 7.What number should Jenna say?
This list shows the age at which 43 U.S. Presidents began their terms. 57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46 Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?
The best way to group these ages into six intervals is from 40-44 to 65-69.
What is a Frequency Distribution Table ?A frequency distribution table gives an idea about the data point or interval and its frequency.
The age of the Presidents given as
57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46
The smallest number ( age) is 42 and the largest number (age ) is 69
To make 6 intervals in this gap of 27 , each interval should be of length 5
Therefore the intervals will be
40-44
45-49
50-54
55-59
60-64
65-69
This is the best way to group into intervals.
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Final answer:
The best way to group the ages of U.S. Presidents into six intervals for a frequency table is by intervals of five years each, starting at age 42 and ending at age 71, to cover the entire range and maintain equal width for all intervals.
Explanation:
When grouping ages into intervals for a frequency table, it's best to have intervals that are of equal width and cover the entire range of data without overlap. For the ages of U.S. Presidents starting their terms, which range from 42 to 69, we could divide this range into six intervals in a way that makes sense for this data set.
First, find the range by subtracting the youngest age from the oldest: 69 - 42 = 27. Next, divide this range by the number of desired intervals (6), which gives us 4.5. We can round this to 5 to make the intervals more practical. Thus, each age interval will span 5 years. Starting at 42, the six intervals would be: 42-46, 47-51, 52-56, 57-61, 62-66, and 67-71.
This grouping covers all the ages and each interval is of equal width, making it easy to interpret the frequency table.
Tickets for the movies are $7 for adults and $4 for children. Fourteen people paid a total of $68 for tickets. How many were adults and how many were children?
A fourth as much as the product of two thirds and 0.8
A fourth as much as the product of two thirds and 0.8 is ²/₁₅
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
First, we will translate this word problem into a mathematical equation.
The product of two thirds and 0.8
[tex]\frac{2}{3} \times 0.8[/tex]
A fourth as much as the product of two thirds and 0.8
[tex]\frac{1}{4} (\frac{2}{3} \times 0.8)[/tex]
[tex]= \frac{1}{4} (\frac{2}{3} \times \frac{4}{5})[/tex]
[tex]= \frac{1}{4} (\frac{2 \times 4}{3 \times 5})[/tex]
[tex]= \frac{1}{4} (\frac{8}{15})[/tex]
[tex]= \frac{1}{4} \times \frac{8}{15}[/tex]
[tex]= \frac{1 \times 8}{4 \times 15}[/tex]
[tex]= \frac{8}{60}[/tex]
[tex]= \frac{8 \div 4}{60 \div 4}[/tex]
[tex]= \boxed {\frac{2}{15}}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
Noah makes ceramic pots for the market. On the weekends he makes 11 more pots than he does during the week. Noah represented the number of pots he makes on weekends using the expression p + 11. Which expression represents the total mumber of pots Noah made one weekend if he made 14 more than his usual number?
4x. (2x^3 — x^2–18x+15) Standard Form
What is 30 divided by half plus 10
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answer:
900
Step-by-step explanation:
Khan academy
Choose the graph that represents the time for which the velocity of the ball will be between –90 and –58 ft/s.
The answer is c because t must be less than 2.5 and more than 1.5.
Find this by separating the inequality into:
-90 < -32t - 10
&
-32t - 10 < -58
Simplify and you get 2.5 and 1.5
Graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have:
The velocity of the ball will be between –90 and –58 ft/s.
Let v be the velocity of the ball:
v lies between -90 and -58
-90 < v < -58
The above expression represents the inequality:
Or
-90 < -32t - 10
t < 2.5
And
-32t - 10 < -58
t > 1.5
The number line will be:
Open the circle on the number 1.5 and open circle at 2.5 and a line was drawn between this point.
Thus, graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
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