Problem #1 - Luca went
grocery shopping for
some last-minute picnic
supplies. He knows that
the sliced turkey was
$3.50 per 1 1/4-pounds
and coleslaw was $1.35
per 1/2 pound. How
much would it cost him if
he bought 3 pounds of
turkey and 1 1/2 -pounds
of coleslaw?
Problem #2 - Fill in the
Why?
The required it would cost $12.45 to buy 3 pounds of turkey and 1 1/2 pounds of coleslaw.
What are expression models?The expression model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
To calculate the cost of the turkey, we need to find the price per pound and then multiply it by the number of pounds. The price per pound is,
= $3.50 ÷ (1 1/4 pounds)
= $2.80 per pound
To find the cost of 3 pounds of turkey, we can multiply the price per pound by the number of pounds:
= 3 pounds × $2.80 per pound = $8.40
To find the cost of the coleslaw, we can simply multiply the price per half pound by the number of half pounds,
1 1/2 pounds = 3 half pounds
= 3 half pounds × $1.35 per half pound
= $4.05
Finally, we can add the cost of the turkey and the coleslaw to find the total cost:
$8.40 + $4.05 = $12.45
Therefore, it would cost $12.45 to buy 3 pounds of turkey and 1 1/2 pounds of coleslaw.
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suzy borrows $4500 and agrees to repay it all in equal monthly instalments over 3 years. Simple interest at 7.2% p.a is charged on a loan. find the amount of each instalment
The amount of Suzy's instalment every month if it is agreed to repay equal amount monthly is $152
What is the amount of each instalment?Simple interest = principal × rate × time
= 4500 × 0.072 × 3
= $972
Total amount to repay = $4500 + $972
= $5472
Repayment time = 3 years
Suzy will repay every month
3 years= 12 months × 3
= 36 months
Since,
the repayment is equal every month
Amount of instalment every month= $5472 / 36
= $152
Therefore, Suzy will repay $152 each month instalmentally.
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How many digits do you need to number all 178 buildings on a street?
You need 4 digits to number all 178 buildings on a street.
Explain Digits.In the decimal number system, digits are the symbols used to represent numbers. The 10 digits of the decimal numeral system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. By utilizing them in various combinations and places, these digits are used to represent all possible decimal integers. A digit's value is also affected by its position in a number according to the place value system. For instance, the digits 1 and 2 in the number 123 each stand for one hundred, twenty, and three respectively. Digits are the fundamental components of numbers and are frequently used in daily life for calculations, measurement, and counting.
To find the number of digits in a number, you can take the logarithm of the number with base 10 and add 1. So, using the logarithm function, you can calculate:
log10(178) + 1 = 2.25 + 1 = 3.25
Therefore, you need 4 digits to number all 178 buildings on a street.
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Which proportion can be used to find the length of sides ik
The proportion i/k = 12 can be used to find the length of sides i and k if the perimeter is 12 units. To solve for the length of each side, the equation i + k = 12 is used, and then the two sides are divided by each other to get the proportion i/k = 12.
The proportion i/k = 12 can be used to find the length of sides i and k of a shape if the perimeter is 12 units. In order to solve for the length of each side, the equation i + k = 12 is used to determine the sum of the sides. The two sides are then divided by each other, resulting in the proportion i/k = 12. This proportion can then be used to find the length of sides i and k. For example, if the length of side i is 8, then the length of side k is 4. This can be determined by dividing 8 by 4, which results in the proportion i/k = 2. If the perimeter is 12 units, then the equation i + k = 12 can be used to determine that the length of side i is 6 and the length of side k is 6, since 6 + 6 = 12. The proportion i/k = 12 can then be used to confirm that the length of side i is 6 and the length of side k is 6.
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The complete question is
Which proportion can be used to find the length of sides ik if the perimeter is 12 units?
80% of a number is x. What is 100% of the number? Assume x>0
100% of the number is: the number x ÷ 0.8 × 1 = the number If 80% of a number is x, then the number can be found by dividing x by the percentage as a decimal.
To convert a percentage to a decimal, divide the percentage by 100.
So, if 80% of the number is x, then:
x ÷ 0.8 = the number
In other words, to find the whole number, we need to divide the part (x) by the percentage as a decimal (0.8).
Once we have the whole number, we can find 100% of it by simply multiplying the whole number by 1.
So, 100% of the number is:
the number x ÷ 0.8 × 1 = the number
In conclusion, if 80% of a number is known, the whole number can be found by dividing the part by the percentage as a decimal, and 100% of the number can be found by simply multiplying the whole number by 1. Understanding the concept of percentage and the ability to convert between percentages, decimals, and whole numbers is an important skill in various areas of life and work.
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A used car lot sold 84 vehicles last month, and 8 of them were minivans. What is the experimental probability that the next vehicle sold will be a minivan?
Write your answer as a fraction or whole number.
Answer:
2/21
simplify 8/84
Answer:
The experimental probability of the next vehicle sold being a minivan is 8/84 = 1/10.
Step-by-step explanation:
The experimental probability of an event can be calculated by dividing the number of successful outcomes by the total number of trials. In this case, we want to find the probability of selling a minivan, so we want to find the number of minivans sold divided by the total number of vehicles sold.
Therefore, the experimental probability can be calculated as follows:
Number of minivans sold / Total number of vehicles sold = 8 / 84
So, the experimental probability that the next vehicle sold will be a minivan is 8/84.
Rahul drives 10 miles in 20 minutes. If he drove three hours in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Rahul drive in total?
180
180
How far would Rahul drive in 180 minutes?
The distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
What is meant by the speed of an object?
A scalar quantity, speed is defined as the magnitude of the change in an object's location over time. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. Zero speed refers to an object that is not moving at all.
The formula of speed = Distance covered /Time taken
Given,
Distance travelled = 10 miles
Time taken to travel 10 miles = 20 minutes
Speed = Distance/ time = 10/20 = 0.5miles/min
Now given the speed remains constant throughout the journey.
So the distance travelled in 3 hours = 3 * 60 = 180 minutes
Distance = speed * time = 0.5 * 180 = 90 miles.
Therefore the distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.
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on the z table with a 90% confidence interval, what is 1.645 called? group of answer choices critical value confidence interval margin of error point estimate
On the z-table with a 90% confidence interval, the value 1.645 is called the critical value. The critical value is used to determine the boundary values for the confidence interval. Correct option is A.
In a confidence interval, we use sample data to estimate the true population parameter with a certain degree of certainty or confidence. The critical value is determined based on the desired confidence level and the degrees of freedom (sample size - 1) of the distribution.
For example, if we want a 90% confidence interval, we use the z-table to find the critical value that corresponds to a probability of 0.05 in the tail of the distribution. The critical value represents the number of standard errors that correspond to the probability in the tail of the distribution.
Once we have determined the critical value, we can use it to find the margin of error for the confidence interval, which represents the range of values within which the true population parameter is likely to lie. The margin of error is calculated by multiplying the critical value by the standard error of the sample statistic.
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Complete question is:
On the z table with a 90% confidence interval, what is 1.645 called? group of answer choices
a. critical value
b. confidence interval
c. margin of error point
d. estimate
State if the lines are Parallel, Perpendicular, or Neither. 6x-12y=24 4x+2y=8
Answer:
Step-by-step explanation:
The lines are neither parallel nor perpendicular.
Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if the product of their slopes is -1.
To find the slope of a line given in the form of Ax + By = C, we can rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.
The first line, 6x - 12y = 24, can be rearranged into slope-intercept form as follows:
12y = -6x + 24
y = -0.5x + 2
The slope of the first line is -0.5.
The second line, 4x + 2y = 8, can be rearranged into slope-intercept form as follows:
2y = -4x + 8
y = -2x + 4
The slope of the second line is -2.
Since the product of the slopes is not -1, the lines are not perpendicular. And since the slopes are not the same, the lines are not parallel. So, the lines are neither parallel nor perpendicular.
what is the standard error? group of answer choices the standard error is the standard deviation of the sampling distribution the standard error is a measure of how representative a sample statistic is likely to be of the population parameter. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
The correct option is "the standard error is the standard deviation of the sampling distribution." Correct option is A.
The standard error is a measure of the variability of a sampling distribution, which is the distribution of sample statistics (e.g., mean, proportion) that would be obtained from multiple random samples of the same size from the same population.
The standard error represents the standard deviation of the sampling distribution, and it provides a measure of the precision of the sample statistic in estimating the population parameter.
The standard error is not the same as the standard deviation of the sample, which is a measure of the variability of the individual observations in the sample.
The standard deviation of the sample is typically used to estimate the standard deviation of the population, while the standard error is used to estimate the variability of the sample statistic and to construct confidence intervals or perform hypothesis tests.
While the other options are related to the concept of the standard error, they are not equivalent or fully accurate descriptions of what the standard error represents.
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Complete question is:
What is the standard error?
group of answer choices
A. the standard error is the standard deviation of the sampling distribution
B. the standard error is a measure of how representative a sample statistic is likely to be of the population parameter.
C. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
Find the value of each trigonometric ratio. Express your answer as a fraction in lowest terms.
The value of the trigonometric ratios are
1. sin C = 21/29
2. sin C = 3/5
3. cos C = 12/13
4. cos C = 8/17
5. tan A = 12/35
6. tan X = 4/3
How to find the trigonometric ratiosThe trigonometry problem in a triangle is worked using an acronym SOH CAH TOA, this acronym means:
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
1. sin C
sin C = opposite / hypotenuse = 21/29
3. cos C = 12/13
cos C = adjacent / hypotenuse = 36/39 = 12/13 to the lowest term
6. tan X = 4/3
tan X = opposite / adjacent = 36/27 = 4/3 to the lowest term
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Alice is willing to spend $30 on a pair of jeans, and has a coupon for $10 off she found online. She selects and purchases a $35 pair of jeans, pre-discount. Jeff finds some steaks for $16 for which he would have been willing to pay $20. The butcher notices the meat is near the expiration Jeffs surplus: date and gives him an extra 75% off.
Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.
Let's calculate the final amount paid by Alice and Jeff for their purchases.
Alice:
Alice has a budget of $30 for a pair of jeans, and a coupon for $10 off.The price of the jeans she selects is $35 before the coupon.To find the final price she paid, we need to subtract the coupon discount from the original price of the jeans: $35 - $10 = $25.So Alice paid $25 for her pair of jeans.Jeff:
Jeff finds a pack of steaks for $16 and is willing to pay up to $20.This means he has a surplus of $20 - $16 = $4 that he is willing to spend on the steaks.The butcher notices the meat is near the expiration date and gives Jeff an extra 75% off.To calculate the discount, we first need to find 75% of the original price: 0.75 * $16 = $12.So Jeff gets a discount of $12, and the final price he paid is the original price minus the discount: $16 - $12 = $4.Therefore, Jeff paid $4 for the steaks.So, Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.
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The temperature in Wintergreen Resort in Virginia fell from 15.8
degrees Celsius to - 2.7 degrees Celsius. What is the difference
between the two temperatures?
The term "difference" os the result of subtracting one number from another.
So in other terms you want to know what would be the result of subtracting -4.6 from 13.5 :
13.5 - -4.6 = Difference between the two temperatures
Two minus signs turn into a positive sign so :
13.5 - -4.6 =
13.5 + 4.6 =
18.1 = Difference between the two temperatures
Your answer is : The difference between the two temperatures is 18.1
Sorry for the grease LOL was eating a big mac also this is urgent
Jada's grandparents started a savings account for her in 2010. The table shows the
amount in the account each year.
If this relationship is graphed with the year on the horizontal axis and the amount in
dollars on the vertical axis, what is the vertical intercept? What does it mean in this
context?
2
year
2010
2012
2014
2016
1gnibasi
Seadsh
amount in dollars
The vertical intercept for the table showing the relationship for Jada's grandparents starting a savings account for her is starting savings amount in the account of $ 600.
What is the vertical intercept in a graph ?The vertical intercept in a graph is the point where a line intersects the vertical axis of the coordinate plane. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
The vertical intercept would therefore be first amount in the savings account by Jada's grandparents which is the $ 600. This is the amount when x = 0 or rather when x was the starting year of 2006.
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a car depreciated 1000 each year it was owed and driven. what type of depreciation is this?
Answer:
Straight line Depreciation
HELP!!! DUE TONIGHT!
Answer:
33.912
Step-by-step explanation:
U have to multiply 10.8 x 3.14 to get the answer
Hopefully this helps and if it did pls mark me as the brainlest
Find the zeros of g(x) = 2x² + 32.
The zeros of g are x =
and x =
When Jackie woke up, the temperature was 70 °F. For the next 5 hours, the temperature rose by 4 °F each hour. Write an equation in the form y = mx + b that Jackie can use to find the temperature x number of hours after she woke up.
An equation to find the temperature after x number hours of waking up for Jackie is Temperature ( x ) = 4 x + 70
How to find the equation ?The equation which takes the form y = mx + b means that in relation to the temperature when Jackie woke up:
y = current temperature after x hours
x = number of hours after waking up
m = change in temperature per hour
b = starting temperature when Jackie woke up
The equation to find the temperature after x hours is therefore:
Temperature ( x ) = 4 x + 70
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c. 3x - y = 7
y = 3x - 2
Answer:
Step-by-step explanation:
3x- (3x-2)=7
- (3x-2) = -3x+2
3x-3x=0x
so the answer is zero or imposible becasue nothing can be times by zero
12, x, y, 324, 972, find the sum of x and y (a) 144 (b) 52 (c) 75 (d) 109
Answer: The value of the sum of x and y is (a) 144.
Step-by-step explanation:
Given, The sequence is a Geometric Sequence.
Initially,
=> 4x3 , x , y , 324, 324x3
=> 4x3, x, y, 4x3x3x3x3, 4x3x3x3x3x3
From above,
We can deduce that,
=> x = 4 x 3 x 3
=> x = 36
Also,
=> y = 4 x 3 x 3 x 3
=> y = 108
The values of x and y are 36 and 108
Now, We can evaluate the sum of x and y,
=> x + y = 36 + 108
=> x + y = 144
Therefore, The sum of x and y is 144. Hence, option (a) is correct.
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Can someone help a stoned brotha out
How many digits of the form x15y is di ivsble by 15
There are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.
A number is divisible by 15 if and only if it is divisible by both 3 and 5.For a number of the form x15y to be divisible by 5, y must be either 0 or 5.
For a number of the form x15y to be divisible by 3, the sum of its digits must be divisible by 3. Since the sum of the digits is x + 1 + 5 + y = x + y + 6, x + y must be either 0, 3, 6, 9, 12, or 15.
So, we need to find all possible values of x and y such that x + y is one of these six values, and y is either 0 or 5.
If y = 0, then x must be one of the numbers 0, 3, 6, 9, 12, 15, 18, or 21, for a total of 8 possibilities.
If y = 5, then x must be one of the numbers 2, 5, 8, 11, 14, 17, or 20, for a total of 7 possibilities.
Therefore, there are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.
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Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. Write equivalent ratios to determine the amount of green and white paint she will need to purchase.
Based on the information, Wendy will need to purchase 48 quarts of paint
How to calculate the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house.
The amount of paint needed will be:
= 4/1 × 12
= 48 quarts
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Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. a. Write equivalent ratios to determine the amount of green and white paint she will need to purchase. b. If there are 4 quarts in 1 gallon, how many quarts of paint does she need to purchase
A line is drawn tangent to a circle of radius 8 with the origin as its center, passing through the paint (12,0). Find the point where the line touches the circle. NOTE: the tangent line will be perpendicular to the radical line from the origin to the tangent point. Use the relation between the slopes to find the point
The radius line intersects the circle at (4, 8) because the tangent line's slope, which is -1/3, is perpendicular to the radius line's slope of (0, 8), which is 0.
1. Use m = 0 to calculate the slope of the line through point (12, 0).
2. Calculate the radical line's angle between the origin and the tangent point: m = ∞
3. To determine the location where the line touches the circle, use the relationship between the slopes: M2 = -1/M1 = -1/0 = - since M1 M2 = -1
4. To determine a point's coordinates, use the equation for a circle: (x - 8)2 + (y - 8)2 = 82, so (4, 8) (4, 8)
We can use the relationship between the slopes of the tangent line and the radical line from the origin to the tangent point to determine the location where the line contacts the circle. Since the tangent line crosses through point (12,0), its slope is equal to zero. Since the radical line slopes at m2 =, m1 m2 = -1. Accordingly, m2 = -1/m1 = -1/0 = -∞.The coordinates of the spot where the line touches the circle can then be determined using the equation for a circle. (x - 8)2 + (y - 8)2 = 82 is the equation for a circle having the origin as its center and a radius of 8. The coordinates of the place where the line intersects the circle are (4, 8), which can be obtained by substituting in the values for m1 and m2.
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a plane left kennedy airport on tuesday morning for a 595-mile, 5-hour trip. for the first part of the trip, the average speed was 110 mph. for the remainder of the trip, the average speed was 125 mph. how long did the plane fly at each speed? first part of trip h second part of trip h
The plane flew at 110 mph for 4.55 hours and at 125 mph for 0.45 hours.
The first step in solving this problem is to recognize that we can use the formula
=> speed = distance/time
to find the time it took for the plane to travel at each speed. Let's denote the time the plane traveled at the first speed (110 mph) as t1, and the time it traveled at the second speed (125 mph) as t2.
We know that the total distance traveled was 595 miles, and the total time taken was 5 hours. Using the formula for average speed, we can write:
Average speed = total distance / total time
Therefore,
Average speed = 595 / 5 = 119 mph
Now we can use the information about the two speeds to set up a system of equations. The first equation relates the total distance traveled at the first speed to the time it took:
110t₁ = d₁
where d1 is the distance traveled at the first speed. Similarly, the second equation relates the total distance traveled at the second speed to the time it took:
125t₂ = d₂
where d₂ is the distance traveled at the second speed.
The total time taken is the sum of the times taken at each speed:
t₁ + t₂ = 5
We now have three equations and three unknowns (t₁, t₂, and d₂). We can use the first two equations to eliminate d₁ and d₂, and then solve for t₁ and t₂.
Multiplying the first equation by 125/110, we get:
125/110 * 110t₁ = 125/110 * d₁
125t₁/110 = d₂
Substituting d₂ in the third equation, we get:
t₁ + 125t₁/110 = 5
Multiplying both sides by 110, we get:
121t₁ = 550
Solving for t₁, we get:
t₁ = 4.55 hours
Substituting t₁ in the third equation, we get:
t₂ = 0.45 hours
Therefore, the plane flew at 110 mph for 4.55 hours and at 125 mph for 0.45 hours.
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Complete Question:
A plane left Kennedy Airport tuesday morning for a 595−mileˏ 5−hour trip.
For the first part of the tripˏ the average speed was 110 mph.
For the remainder of the tripˏ the average speed was 125 mph. How long did the plane fly at each speed.
Andrew ran 0.75 miles at basketball practice.
Write 0.75 miles as a fraction in simplest form.
of a mile
Write 0.75 miles as a percent.
% of a mile
Answer:
Fraction 3/4 percent 75%
Step-by-step explanation:
.75 in simplest form is 3/4
A cylinder has a radius of 2.5meters. Its volume is 37.5\pi cubic meters. What is the height of the cylinder?
Answer: height = 1.91 m
Step-by-step explanation: Using the formula
V=πr2h
Solving for h
h=V
πr2=37.5
π·2.52≈1.90986m
21. Given h(x) = -x-14, if h(x) = -2, find x.
Answer:
Step-by-step explanation:
stop searching answers poopers use ur mind
Answer:
-12
Step-by-step explanation:
Substitute x with -2
-(-2)-14
2-14 = -12
The concession stand at a football game had 3,903 soft pretzels and 2,804 hard pretzels before the game began. When they count the food after the game, there is a total of 1,683 pretzels left. How many pretzels were sold?
Answer:
5024
Step-by-step explanation:
3903+2804= 6707
6707-1683=5024
three coplanar circles intersect as shown. what is the maximum number of points on the circles that a line passing through all three circles can touch?
The maximum number of points on the circles that a line passing through all three circles can touch is 36.
Two circles may cross in two points, one point, or no points on a aeroplane, digression circles are coplanar circles that cross at a single point.Concentric circles are coplanar circles that share a common centre.
You can select any two circles in (₂³) ways and each pair will intersect at 2 points. Therefore total 3*2=6 points.
Similarly, 4 lines will intersect at (₂⁴)=6
points.
Now each line will intersect at 2 points with a circle. And since we can select a circle in (³₁) ways and a line in (₁⁴) ways, therefore total (₁³)∗(₁⁴)∗2=24 points they will intersect.
Therefore, total number of intersection points = 6 + 6 + 24 = 36 points.
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