Answer: 24 cups of sugar
Step-by-step explanation: you multiple the orginal amount neede for one batch by 8
8*3=24
A real estate agent sold a house for $315,000 last week. If her commission is 1.25% of the selling price of the home, find the amount of her commission?
The required amount of her commission is given as $3937.5.
Given that,
A real estate agent sold a house for $315,000 last week. The commission is 1.25% of the selling price of the home,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Commission = 1.25% of $315000
Commission = 1.25× 315000/100
Commission = $3,937.5
Thus, the required amount of her commission is given as $3937.5.
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Quadrilateral IJKL is similar to quadrilateral MNOP. Find the measure of side PM. Round your answer to the nearest tenth if necessary.
Answer: 76.2
Step-by-step explanation:
54/17=3.176
3.176=the scale factor
3.176(24)=76.224
Rounded=76.2
Answer:
PM = 76.2 units---------------------------------------------------
If two figures are similar then their corresponding sides have same ratio.
Find ratios:
PM / LI = ON / KJSubstitute and find the value of PM:
PM / 24 = 54 / 17PM = 24*54/17PM = 76.2 (rounded)Find a point on the line and the line's slope.
y-5=-2/(x-3)
Answer:
Slope: - 4/3
Point (4,1)
Step-by-step explanation:
hope this helps
What is the equation of the line that passes through the point (-3,-3)(−3,−3) and has a slope of 33?
The required equation of the line having a slope of 33 and passing through (-3, - 3) is y = 33x + 96.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Let the required line be y = mx + b.
∴ - 3 = (33)(-3) + b.
- 3 = - 99 + b.
b = 96.
∴ y = 33x + 96 is the required line.
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a kite is flying 120 ft above the ground. the length of the string to the kite is 200 feet, measured from the ground. find the angle, to the nearest degree, that the string makes with the ground.\
The angle, to the degree, that the string makes with the ground is
34.33.
A right-angled triangle can be formed by the string, the height of the kite, and the horizontal distance along the ground to a point directly beneath the kite.
The string represents the hypotenuse (200 feet), and the height (120 feet) represents the opposite side.
The trigonometric ratio sin can be used to calculate the angle between the string and the ground.
sinθ= Perpendicular/hypotenuse
sinθ=120/200
=0.6
Now sin(0.6) = 0.5646
sinθ=0.5646
therefore ,θ
=sin⁻¹(0.5646)
=34.33°
Heights and Distances is a study of Trigonometry applications. It has many real-world applications, such as measuring the height of an object, the depth of an object, the distance between two celestial objects, and so on.
Trigonometric formulas and ratios are useful in the study of heights and distances.
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the perimeters of a rectangle and an equilateral triangle are equal. what is the equation for this scenario?rectangle’s perimeter:equilateral triangle’s perimeter:scenario’s equation:
The total length of a boundary defines the perimeter of an equilateral triangle.
What is the Perimeter of an Equilateral Triangle?The total of the three sides makes up the perimeter of an equilateral triangle. The following fundamental characteristics define a triangle as being equilateral:The three sides are equal.There is a 60° angle between all three.The sides of the triangle PQ = QR = RP in the following illustration have equal lengths. The triangle's angles are also equal in addition to this. An equilateral triangle is what this is. An equilateral triangle's perimeter is now equal to 3a, where a denotes one of the triangle's sides.Perimeter of Equilateral Triangle Formula : P = 3a, where 'a' stands for one of the triangle's sides, is a simple formula for calculating an equilateral triangle's perimeter. An equilateral triangle has three equal sides, hence the sum is equal to three equal sides, or 3a.Additional equilateral triangle formulas include the following: When we need to determine a triangle's height from its sides, we can apply the following formula: Equilateral Triangle Height = (3a)/2The semi-perimeter of an equilateral triangle must be determined in a few situations. Half of a perimeter, or semi-perimeter, is equal to 3a/2, which is derived using the formula semi-perimeter = (a + a + a)/2.To Learn more About equilateral triangle refer to:
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Answer:
The equation for scenario is 2(l + b) = 3a
The rectangle’s perimeter is 2(l + b)
The equilateral triangle’s perimeter is 3a
What is perimeter ?
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
According to question
The perimeters of a rectangle and an equilateral triangle are equal.
So
let,
The length and breadth of the rectangle are l & b
And
Side of an equilateral triangle is a
Now
The rectangle’s perimeter = 2(length + breadth)
⇒ 2(l + b)
And
The equilateral triangle’s perimeter = Sum of All sides
⇒ a + a + a
⇒ 3a
Therefore
perimeters of a rectangle = perimeters an equilateral triangle
2(l + b) = 3a
hence, 2(l + b) = 3a is the equation which show that perimeter of rectangle and equilateral triangle is equal.
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has mean 20.2 years and standard deviation 1.60 years. of all of those enrolled in the course, 54 percent are men and 46 percent are women. what is the mean age of the combined distribution of both men and women in the course?
The mean age of the combined distribution of both men and women in the course is 20.47 years
What is average/mean ?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
Mean age of men , M = 20.7 years
Mean age of Women , W = 20.2 years
Percentage of Men = 54%
Percentage of Women = 46%
Recall, :
Mean, μ = np
The mean age of men in the distribution = (20.7 × 54%) = 11.178 years
The mean age of women in the distribution = (20.2 × 46%) = 9.292 years
The mean age of the combined distribution is :
11.178 + 9.292 = 20.47 years
Therefore, the mean age of the combined distribution is 20.47 years
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A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate. Using hospital birth records, she selects a simple random sample of 200 couples who had children within the first 2 years of marriage. Following up on these couples, she finds that 80 couples are divorced within 5 years. Let p= the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years. What is a 90% plus four confidence interval for the proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years?
Question options:
0.402 ± 0.088
0.402 ± 0.067
0.402 ± 0.057
0.402 ± 0.035
the confidence interval for 90% plus four is 0.4±0.067
what is confidence interval?It refers to an average value of our estimated value plus and minus the variation of the estimated value.
why confidence interval is important in the statistics?In the statistics confidence level indicates the level of reliability of a particular estimation.
Let, p is the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.
as per above question p=80
number of random samples = n
n=200
now q is the ratio of p/ number of random samples
q= 80/200 = .04
now confidence interval for 90% plus 4 that means 94% confidence interval is calculated by the formula = q±Zc√{q(1-q)/n}
= 0.4±1.94√{0.4(1-0.4)/200}
where, zc is the z-score for 94% confidence interval and zc=1.94,
hence, confidence interval for 94% = 0.4±0.067
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A mountaineer is climbing on a cliff. She is 400 feet above the ground. If she climbs up, this will be a positive change. If she climbs down, this will be a negative change.
Complete the table.
Answer:
I added a picture, hope this helps!
Step-by-step explanation:
Let me know if you need to show work
25 { x }^{ 2 } +36 { y }^{ 2 } True or false: The polynomial is a difference of squares.
The polynomial 25x² + 36y² is the sum of the squares.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, 25x² + 36y² which can be written as,
= 5²x² + 6²y².
= (5x)² + (6y)² it is the sum of the squares, The difference of squares would be (5x)² - (6y)².
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A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in hundreds of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 44.4765 Standard Error Observations 30,0000 ANOVA SS MS Significance F 1 171062.9193 171062.9193 86.4759 Regression 0.0000 28 55388.4309 1978.1582 Residual Total 29 226451.3503 Coefficients Standard Emor t Stat P-value Lower 95% Upper 95% 95.0614 26.9183 3.5315 0.0015 150.2009 39,9218 intercept 4.5513 Download 3,7297 9.2992 0.0000 0.4011 2.9082
a) Write down the regression equation.
b) What is the correct interpretation for the slope coefficient?
c) Predict the revenue when the number of downloads is 30,000.
Answer: ______________________________
d) What is the correct interpretation for the coefficient of determination (R2)?
e) The 95% confidence interval estimate for the population slope is (______________ , ______________)
f) Is there sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance? Give a reason why.
Here is sufficient evidence that revenue and the number of downloads are linearly related.
A computer software developer would like to use the number of downloads for the trial version of his new shareware to predict the amount of revenue.
The Null hypothesis is the common statistical theory that asserts that no statistical relationship or significance exist between two sets of observed data and measure phenomena based on a single observed variable.
Therefore the null hypothesis become,
H₀ : ρ₁ = 0
and the adjacent hypothesis will become,
H₁ : ρ ≠ 0
Now we will calculate test statistic,
t = r × [tex]\sqrt{\frac{n-2}{1-r^{2} } }[/tex]
= (0.8691) × [tex]\sqrt{\frac{30 - 2}{0.1309^{2} } }[/tex]
t = 9.2974
we know that degree of freedom = n - 2 = 28
p-value at t = 9.2974 is 0.00
α = 0.05
since p-value < α
so null hypothesis will be rejected.
Hence we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.
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In a park, the number of plants increased by 9% over the previous year. If the number of plants now is 62, 130, how many plants were there in the previous year?
Answer:
55.8,117
Step-by-step explanation:
62 times 0.9 is 55.8
130 times 0.9 is 117
I hope this helps!
Mark did a survey.
He asked pupils in his school:
‘Do you like the colour of the school uniform?’
Mark asked this question to 40 pupils in year 11
25% said ‘Yes’. 50% said ‘No’. The rest said ‘Don’t know’.
Complete the table to show how many pupils from year 11 gave each answer.
The following numbers will be illustrated in the table:
Those that said yes = 10
Those that said no = 20
Those that said don't know = 10
How to illustrate the percentage?It should simony be noted that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Number of pupil = 40
25% said ‘Yes’. This will be:
= 25% × 40.
= 10
50% said ‘No’. This will be:
= 50% × 40
= 20
The rest said ‘Don’t know’. This will be:
= 25% × 40
= 10
In conclusion, those who said yes are 10 while those who said no are 20.
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Which is an example of a defined term A. Point B. Line C. Ray D. Plane
Answer: c:ray
Step-by-step explanation:
A ray is like a line, but the line takes off in one direction to infinity while the other side is like a line segment. The end of the line is called the endpoint. That's why it is a defined term.
Work out the size of angle 0.
Give reasons for your answer.
Answer:
θ = 56°
Step-by-step explanation:
As OA and OB are both radii, triangle AOB is an isosceles triangle:
⇒ m∠ABO = m∠OAB = 48°
Interior angles of a triangle sum to 180°:
⇒ m∠ABO + m∠OAB + m∠AOB = 180°
⇒ 48° + 48° + m∠AOB = 180°
⇒ m∠AOB = 180° - 48° - 48°
⇒ m∠AOB = 84°
Angles on a straight line sum to 180°:
⇒ m∠AOB + m∠DOB = 180°
⇒ 84° + m∠DOB = 180°
⇒ m∠DOB = 180° - 84°
⇒ m∠DOB = 96°
The tangent of a circle is always perpendicular to the radius.
Therefore, tangent BC is perpendicular to radius OB, and tangent DE is perpendicular to radius OD, so:
m∠OBC = 90°m∠ODE = 90°OBCD is a quadrilateral.
The interior angles of a quadrilateral sum to 360°:
⇒ m∠OBC + m∠BCD + m∠CDO + m∠DOB = 360°
⇒ 90° + θ + 28° + 90° + 96° = 360°
⇒ θ + 304° = 360°
⇒ θ = 360° - 304°
⇒ θ = 56°
Which of the following is the vertex form of Y = X² - 2x + 5 *?
(x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.
What is the vertex form?A quadratic function has the vertex form f(x) = a(x - h)2 + k, where a, h, and k are constants.
Obtain the equation y = ax2 + bx + c.
Determine -b / 2A.
The vertex's x-coordinate is given here.
Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate.
The vertex's y-coordinate is given here.
So, we have the equation:
Y = X² - 2x + 5
Now, calculate as follows:
⇒ y = (x2 - 2x + 1) + 5 -1
⇒ y - 4 = (x -1)2
⇒ (x -1)2 = y - 4
Therefore, (x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.
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Determine whether the geometric series is convergent or divergent. 10 ? 4 + 1.6 - 0.64 + ... convergent divergen
The series in question converges.
Convergent divergent series: what are they?If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on rising or dropping as the terms of the series go to infinity, it is said to be divergent.
The geometric sequence is as follows:
10 - 4 + 1.6 - 0.64 +...
If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.
The common ratio in this case is
r = -4/10
r = -0.4, or -1 -0.4 1.
The presented series is hence convergent.
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Evaluate the logarithm
Question:
[tex] ln\dfrac{1}{\sqrt{e^{3}}}=x[/tex]To find :
Value of xsolution:
[tex] ln\dfrac{1}{\sqrt{e^{3}}}=x\\\\ e^{^{({ln\dfrac{1}{\sqrt{e^{3}}}})}}=e^{x}\\\\ \dfrac{1}{\sqrt{e^{3}}}=e^{x} \\\\ (\dfrac{1}{\sqrt{e^{3}}})^{2}=e^{2x}\\\\ \dfrac{1}{e^{3}}=e^{2x}\\\\ e^{-3}=e^{2x}\\\\ -3=2x \\\\\sf{x=\dfrac{-3}{2}} [/tex]
final answer:
[tex]\pmb{\dfrac{-3}{2}} [/tex]HELPP 65 POINTS I NEED THEM ALL
It can be expensive to go to the movie theater. The scatter plot shown here gives the average cost in
U.S. dollars of a movie ticket in the U.S. for each year from 1980 to 2013. Using this data, how much do
you think a movie ticket will cost in the years 2020 and 2030? Download the worksheet and complete it.
1. How has the cost of a movie ticket changed over the last 30 years? What has been the general
trend? How can you tell this from the graph? (2 points)
2. What years did the cost of movie ticket decrease compared to the year before? How can you tell
from the graph when the price is decreasing? (2 points)
Student Name:
Predicting Movie Ticket Costs Activity
3. There was a time where the cost of a movie ticket stayed relatively the same over several years.
For what years did the cost stay relatively the same? How can you tell this from the graph? (2
points)
4. The graph could be divided up into three different periods of relatively consistent ticket price
change: The years 1980 – 1988, 1989 – 1993 and 1994 – 2011. Can you find a typical rate of
change in the price of a ticket for each of these time periods? In other words, on average, by
how much did the price of a ticket increase by each year during each of these time periods?
(2 points)
5. Predict the cost of a ticket in 2012 – 2015. Plot your predictions and give your actual predictions
for each year below. How did you determine how much a ticket would cost each year? (2 points)
6. What might have been the cost of a ticket during the years 1975 – 1979? Plot your estimates on
the grid and give your actual predictions for each year below. How did you determine how much
a ticket would cost each year? (2 points)
Predicting Movie Ticket Costs Activity
7. Find a line of best fit to represent the data. Let y = ticket price and x = the number of years since
1980 (1980 is year zero, 1981 is year one). Approximate a line to represent the data, a slope, a y-intercept and equation that models your line of best fit. (2 points)
8. Use your equation (or graph or a table) to predict the cost of a movie ticket in the years 2020
and 2030. Be sure to show how you came to each answer. (2 points)
Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.
What do you mean by rates?
A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
1. Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.
2. From 1988 to 1989 the cost of a ticket decreased. Also from 1991 to 1992 the cost decreased a little. The graph slants a little downward.\
3. From 1990 to 1994 the cost stayed pretty much the same. Those years on the graph look almost level... not sloping upward or downward.
4. 1980-1988 price increased from about $2.75 to about $4.25 $1.50 over 8 years = $0.19 per year 1989-1993 price increased from about $4.00 to about $4.20 = $0.20 over 4 years = $0.05 per year 1994-2011 price increased from about $4.20 to about $8.00 $3.80 over 7 years = $0.54 per year
5. Maybe 2012 will be $8.20, 2013 will be $8.30, 2014 will be $8.50, 2015 will be $8.60 ish
Maybe I should make the price go up about $0.17 cents per year ... on average.
6. 1979 maybe $2.52
1978 maybe $2.36
1977 maybe $2.19
1976 maybe $2.02
975 maybe $1.85
I figured that the price was going down, on average, at about $0.17 per year.
7. one possibility might be y=$5.30/31 x + $2.70 or y = 0.17x+2.7.
8.Using the equation that we fit to this data y = 0.17x + 2.7 we get 0.17(40) + 2.7= $9.50 for the year 2020 and for the year 2030 we get 0.17(50)+2.7 $11.20
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Answer:
Step-by-step explanation:
its b like this the aetter number g
What is the vertex of this parabola?
Answer:
Correct answer is ([7],[5])
Step-by-step explanation:
For the vertex form of the parabola, y = a(x – h)2 + k, the coordinates (h, k) of the vertex are:
(h, k) = (-b/2a, -D/4a)
where,
a is the coefficient of x2,
b is the coefficient of x,
D = b2 – 4ac is the discriminant of the standard form y = ax2 + bx + c.
There are 95 green balls and 90 red balls in a box. How many balls must be chosen to
be certain we have the following?
One red and one green?
The number of balls that must be chosen to be certain we have One red and one green is; 5 balls.
What is the probability of selection?We are given;
Number of green balls in box = 95 balls
Number of red balls in box = 90 balls
Thus;
Total number of balls in the box = 95 + 90
Total number of balls in the box = 185 balls
Now, the probability of getting one red from selection = 90/185
Probability of getting one green ball = 95/185
P(Red and Green) = P(R) * P(G)
P(R and G) = = (90/185) * (95/185) = 0.2418
However, in this case we will make use of the unitary method which is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Thus, minimum number of balls to get the given selection = 95 - 90 = 5 balls
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15+14+13+12+11+10+9+8+7+6+5+4+3+2+1
Answer:
120
Step-by-step explanation:
Don't know if this is a joke, but have a great day regardless!
In triangle XYZ, mZZ = (5m - 15) and the exterior angle to Z measures (7m + 3). Determine the value of m.
Om=6
Om = 8.5
Om = 15
Om = 16
The value of m in the triangle XYZ is 16. option D
How to determine the valueIt is important to note that the sum of angles in a triangle is 180 degrees.
From the information given, we have that;
Angle MZ is the exterior angle = (5m - 15)Angle Z is the interior angle = 7m + 3Then we have that;
Angle MZ + Angle Z = 180
Now, substitute the values into the formula, we have;
(5m - 15) + (7m + 3) = 180°
expand the bracket
5m - 15 + 7m + 3 = 180°
collect like terms
12m - 12 = 180°
12m = 180 + 12
Add the like terms
12m = 192
Make 'm' the subject of formula by dividing both sides by 12, we get;
12m/12 = 192/12
m = 16
The value is 16.
Thus, the value is 16
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should a test of statistical significance be conducted before or after computing d and interpreting its value?
Yes, a test of statistical significance be conducted before or after computing d and interpreting its value.
The p-value is an important phrase for hypothesis testing in the context of statistical significance of data.
The p-value is defined as a function of observed sample outcomes that is used to evaluate statistical hypotheses. Before running the test, a threshold value must be chosen.
The significance is a figure that represents the probability that the outcome of a study occurred entirely by chance. The statistical significance can be low or high. It does not always imply practical significance. When a researcher does not use language carefully in their experiment report, the significance may be misconstrued.
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The map given shows the relationship between three streets. Suppose that m21.
+ m2=180.
Are Maple Street and Elm Street parallel? Explain.
Maple Street
Elm Street
River Drive
No because m1 and m42 are supplementary
Yes because m1 and m42 are supplementary
Yes because m1 and m2 are congruent.
No because m 21 and m22 are congruent.
-30
The correct statement regarding whether Maple Street and Elm Street are parallel lines is given as follows:
Yes, because angles 1 and 2 are supplementary.
How to define whether the lines are parallel?Parallel lines are two lines that do not intersect, or technically, intersect only at infinity.
In this problem, we have that angles 1 and 2 are supplementary angles, hence:
m<1 + m<2 = 180º
As the sum of the measures of supplementary angles is of 180º.
Then these two angles are classified as consecutive interior angles, meaning that Maple Street and Elm Street are parallel lines cut by the transversal River Drive.
Thus the second option is the correct option.
Missing InformationThe situation is represented by the image shown at the end of the answer.
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At the market, 5 light bulbs cost $9 dollar sign, 9.
How much do 7 light bulbs cost?
Answer: $12.60
Step-by-step explanation:
Take 9 divided by 5 = $1.80 per light bulb
Then take 1.80 times 7 = $12.60
Principal = 6,000, rate of interest = 10% p.a., time = 3 years please solve
Answer:
$7800
Step-by-step explanation:
1 year = 10%
3 years = 30%
30% = 0.3
6000 times 0.3 = $1800
6000 + 1800 = $7800
So, they will pay $7800
Solve for x
8/x = 28/42
Answer:
The answer is 12
Step-by-step explanation:
8/x = 28/42
8/x = 2/3
(8) × 3 = (2) × (x)
2x = 24
2x/2 = 24/2
y = 12
y = 12Thus, The value of y is 12
Answer:
12
Step-by-step explanation:
use the theory of cross multiply
so 8•42=28x
336=28x
x=12
Write an equation for the proportional relationship shown in the table.
Answer:
1. k = y/x
k = 17/0.5
k = 34
y = kx (subtitute the value of k)y = 34x2. k = y/x
k = 34/1
k = 34
y = kx (subtitute the value of k)y = 34x3. k = y/x
k = 51/1.5
k = 34
y = kx (subtitute the value of k)y = 34x4. k = y/x
k = 68/2
k = 34
y = kx (subtitute the value of k)y = 34xCREDITS:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-$89.75 scooter ; 7.25% tax
Answer: $96.25
Step-by-step explanation:
Take 89.75 divided by 100% = 0.8975
Then times 7.25% = $6.5
Total is 89.75 + 6.5 = $96.25
