The original price of the sweater is $48.
Given that, Kate used a 30% off coupon to purchase a sweater.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The cost of sweater is $33.60
Let the original price of the sweater be x
Now, x-30% of x=33.60
⇒ x-30x/100 = 33.60
⇒ x -3x/10 =33.60
⇒ 7x/10 =33.60
⇒ 7x=336.0
⇒ x=48
Therefore, the original price of the sweater is $48.
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4.7.4 pt. 2 Modeling Pumpkin launch, we were covering graphs of quadratic functions please help! Thank you, all the info you need is on part 1 on my account
Considering that the pumpkin is on the ground at x = 0 and x = 50, it is found that:
5. The roots of the quadratic function are: r1 = 0, r2 = 50.
6. The function is written as follows: y = a(x - 0)(x - 50).
7. The leading coefficient is a = -0.0992.
8. The function is: y = -0.0992(x - 0)(x - 50).
9. Applying the distributive property, the function is: y = -0.0992(x² - 50x).
10. The graph is given at the end of the answer.
Building a quadratic function from it's rootsA quadratic function of roots x' and x'' is defined as follows:
y = a(x - x')(x - x'').
In the context of this problem, the roots are the values of x when the pumpkin is on the ground, hence:
x' = 0, x'' = 50.
Hence, considering the roots, the function is written as:
y = a(x - 0)(x - 50).
The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet(mean of the roots), hence the vertex is given by these following coordinates:
(25, 62)
The coordinates are used to find the value of a, which is the leading coefficient of the function, as follows:
62 = a(25² - 50 x 25)
62 = -625a
a = -62/625
a = -0.0992.
Then the equation is written as:
y = -0.0992(x - 0)(x - 50).
The distributive property means that the outer term multiplies each the inside terms, and then the common terms are added, hence the function is:
y = -0.0992(x² - 50x).
Which is sketched at the end of the answer.
Missing informationThe pumpkin is on the ground when x = 0 and x = 50.
The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet.
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The melting point of nitrogen is -210 °C. The melting point of magnesium is 650 °C.
What is the difference in melting points of the two elements?
Answer:
860 degrees
Step-by-step explanation:
-210+210=0
0+650=650
650+210=860
One endpoint of a line segment is (10,-1). The point (7,-2) i s one-third of the way from that endpoint to the other endpoint. Find the other endpoint
The coordinates of the other endpoint of the Line segment is (-2,-5).
If M(x.y) divides the line formed by two points A(a,b) and B(c,d) into a ratio m:n. Then the coordinates of the point M can be found out by using the formula,
x = (mc + na)/(m+n)
y = (md + nb)/(m+n)
This above mentioned formula is known as The section Formula.
The one of the End point of the line is (10,-1) and the point (7,-2) is dividing the line in the ratio of 1:3.
Let us assume the other end point to be (a,b).
Now, applying Section Formula,
7 = [(1)(a)+(3)(10)]/4 and
-2 = [(1)(b)+(3)(-1)]/4
Further solving,
a = -2 and
b = -5
So, the coordinates of the endpoint is (-2,-5).
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The nth term of a sequence is 50-n2. Find the thurd term of the sequence.
The third term of the sequence is 41.
Given,
Tn = 50 - n²
Tn = 50 - (3)²
Tn = 50 - 6
Tn = 41
As the third term is required substitute the value in the main equation 50 - n² which gives T3 = 41.
As the third term is necessary, replace 50 - n² in the main equation, yielding T3 = 41.
Arithmetic Progression is a series of numbers in which the difference between consecutive terms is constant. One approach is to calculate the arithmetic mean. To do this, sum all the values and divide the sum by the number of values. For arithmetic sequences, use the expression a = a1 + (n1) d. where a is the term, a1 is the difference of the first term, and d is the difference of the subsequent term.
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[6-34] the manufacturer of a new fiberglass tire claims that its average life will be at least 40,000 miles. to verify this claim, sample of 15 tires are tested. sample mean was 41.1 (in 1000 miles), and sample standard deviation was 2.50. assuming the measurements were random sample from a normal distribution, calculate 95% one-sided confidence interval for true mean tire life. choose lower-bound or upper-bound, whichever is appropriate. (round to 2 decimals.)
The assumption that the sample means follow a roughly normal distribution is used to calculate a confidence interval for a population mean with a known standard deviation.
A confidence interval gives a range of values that will probably include the actual mean. For example, let's say that our sample has a mean of x=10 and we have generated the 90% confidence interval (5, 15), with EBM = 5. For instance, we might not be able to speak to everyone in Colorado if we wanted to find out the typical age of Colorado residents who enjoy bananas. However, we could conduct in-depth interviews with a representative sample and make an educated guess or calculation to provide us with a range of ages.
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Which equation represents a proportional relationship? responses 14x y=10 fraction 1 over 4 end fraction x plus y equals 10 y=14x y equals fraction 1 over 4 end fraction x y=13x 1 y equals fraction 1 over 3 end fraction plus 1 i don't know.
We identify the proportional relationship because it does not have a constant term, the correct option is:
y = (1/4)x
Which equation represents a proportional relationship?
A proportional relationship between two variables x and y is written as:
y = k*x
Where k is called the constant of proportionality.
Here the options are:
(1/4)x + y = 10 (this is a linear equation)y = (1/4)*x (this is a proportional relation)y = (1/3)*x + 1 (this is a linear equation)The only option that has not a constant term is the second one:
y = (1/4)*x
And that is the proportional relationship.
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Answer:
y=(1/4)x
Step-by-step explanation:
I took the test :)
3-3k+7k=5b solve for x
Hey there!
[tex]3-3k+7k=5b[/tex]
Assuming you're trying to solve for b or k, I'll solve both.
Solve for b:
[tex]3-3k+7k=5b[/tex]
We will need to flip the equation:
[tex]5b=4k+3[/tex]
Now, let's divide both sides by 5:
[tex]\frac{5b}{5} =\frac{4k+3}{5}[/tex]
[tex]b=\frac{4}{5} k+\frac{3}{5}[/tex]
Solve for k:
[tex]3-3k+7k=5b[/tex]
Let's add -3 to both sides:
[tex]4k+3+-3=5b+-3\\4k=5b-3[/tex]
Now, let's divide both sides by 4:
[tex]\frac{4k}{4} =\frac{5b-3}{4}[/tex]
[tex]k=\frac{5}{4} b+\frac{-3}{4}[/tex]
Now, we've solved for b and k.
Hope this helps!
If the two triangles shown below are similar
based on the given information, complete
the similarity statement, otherwise choose
the "Not Similar" button.
C
2 in
4 in
ABCA ~ A
A
8 in
B
G
H
16 in
Answer: Similar by SAS
Step-by-step explanation:
Note that [tex]\frac{AC}{AB}=\frac{JG}{HG}=\frac{1}{4}[/tex].
So, the triangles are similar by SAS (since the congruent angle is included between the proportional sides).
URGENT PLEASE HELP
A triangle is translated 6 units left and then dilated by a factor of 0.5.
Which statement about the triangle's image and pre-image is correct?
A) The image and pre-image are congruent figures because one of the transformations is a rigid transformation, and the other
is not.
B) The image and pre-image are congruent figures because both transformations are rigid transformations.
C) The image and pre-image are not congruent figures because one of the transformations is a rigid transformation, and the
other is not.
D) The image and pre-image are not congruent figures because both transformations are rigid transformations.
A triangle is translated 6 units left and then dilated by a factor of 0.5. the statement about the triangle's image and pre-image that is correct is: The image and pre-image are not congruent figures because one of the transformations is a rigid transformation, and the other is not.
What is a rigid transformation?Transformation is a term that refers to movement of an image from one position to the other.
When the intervals or distances between the points of the image being moved is not altered then the transformation is rigid transformation. However when the interval is altered it is a rigid transformation.
Translation is a rigid transformation while dilation is a non rigid transformation.
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HELP ASAP (100 POINTS)
The equation for the line of best fit for change in temperature, y, to amount of snow, s, is given by ŷ = − 2.6s + 1.1. On Friday, the observed amount of snow was 1.3 inches and the temperature change was 1.2 degrees. Find and interpret the residual.
1.08; The line of best fit underpredicts the temperature change.
−1.08; The line of best fit overpredicts the temperature change.
−3.48; The line of best fit overpredicts the temperature change.
3.48; The line of best fit underpredicts the temperature change.
Answer:
3.48; The line of best fit underpredicts the temperature change.Step-by-step explanation:
ŷ = − 2.6s + 1.1.
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
For s = 1.3
y = 1.2
value of y from the equation, y1:
y1 = -2.6*(1.3) + 1.1
y1 = -3.38 + 1.1
y1 = -2.28
residual value = y - y1
residual value = 1.2 - -2.28
residual value = 1.2 + 2.28
residual value = 3.48Interpretation:
Since the predicted value is far less than the observed value, the line of best fit underpredicts the temperature change.
Answer:
3.48; The line of best fit underpredicts the temperature change.
Step-by-step explanation:
i took the test :)
are lines AC and DF parallel explain
Answer:
yes
Step-by-step explanation:
ac goes straight forever and df does straight forever and they are parallel
17<9+X
O A. x> 8
OB. x > 26
O C. x < 26
O O
D. x < 8
Answer:
A
Step-by-step explanation:
17 < 9 + x ( subtract 9 from both sides )
8 < x , then
x > 8
What is the value of this expression when m = 3 and n=−1?
−4(m−n)2
Answer:
-32
Step-by-step explanation:
m=3 , n=-1 ( given )
then, -4(m-n)2 = -4(3-(-1))2 = -32
Express in decimal notation 4.93 x 10^(3)
The decimal notation of 4.93 x 10³ will be 4930.00.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is;
4.93 x 10³
Now, Solve for decimal notation as;
4.93 x 10³ = 4.93 x 10 x 10 x 10
= 49.3 x 10 x 10
= 493 x 10
= 4930.00
Thus, The decimal notation of 4.93 x 10³ will be 4930.00.
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standard to intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 5y - 6x = 5[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 5y = 6x + 5[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + \frac{5}{5} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Type the missing number to complete the proportion. 80 minutes for 22 songs minutes for 11 songs Submit
80 : 22 :: x : 11
x = (11 x 80) / 22
x = 880/22
x = 40
The missing number is 40
You have saved some money to purchase five different songs to download to your portable music device. Solve an inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars.
If you have saved some money to purchase five different songs to download to your portable music device. The inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars is : 5 x ≤ 20.
InequalityGiven:
Numbers of different songs to download = 5
Cost = $20
Hence,
The inequality is ; 5 x ≤ 20
Now let solve the inequality
5 x ≤ 20
x = 20 /5
x = 4
So,
= x ≤ 4
Therefore the inequality is 5 x ≤ 20.
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between 9 am and 6:36 am, the water in a swimming pool decreased by 8/25 in. assuming that the water level decreased at a constant rate, how much did the water level drop each hour
Answer: 2/15 in/hour
Step-by-step explanation:
[tex]\displaystyle\\1)\ 6:36=\\\\6\frac{36}{60}=\\\\6\frac{3(12)}{5(12)}=\\\\6\frac{3}{5}=\\\\\frac{6*5+3}{5}=\\\\\frac{30+3}{5}=\\\\\frac{33}{5} \ hours[/tex]
[tex]\displaystyle\\2)\ 9-\frac{33}{5} =\\\\\frac{9(5)-33}{5}=\\\\\frac{45-33}{5} =\\\\\frac{12}{5}\ hours[/tex]
[tex]\displaystyle\\3)\ \frac{8}{25}:\frac{12}{5} =\\\\\frac{8}{25}*\frac{5}{12} =\\\\\frac{8(5)}{25(12)} =\\\\\frac{2*4*5}{5*5*4*3} =\\\\\frac{2}{5*3} =\\\\\frac{2}{15}\ in/hour[/tex]
1. Between which two whole numbers is
√12?
Convince Me!
2. Which of the two numbers is a better
estimate for √12? Explain.
The two whole numbers between which is √12 are 3 and 4.
What is an example of a whole number?
Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.
The closest perfect squares near 12 are 16 and 9 which are the perfect squares of 4 and 3 respectively Therefore the root of 12 lies between 3 and 4.
i.e 3 < √12 < 4
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Jaime, ralph, marvin and victor decided to put up a small business. their initial investment is in the ratio of 8:3:12:2 respectively and marvin's had ivested php 240,000. interms of profit they have decided to split them base on the ratio of their investment. in the first three months of their company made a total of php 150,000 profit. based on marvin's initial deposit. how much did victor invested?
Answer:
php 40,000
Step-by-step explanation:
In the ratio, Marvin corresponds to 12 and Victor to 2.
Marvin invested php 240,000.
His part of the ratio is 12.
240,000/12 = 20,000
Victor's part in the ratio is 2.
Victor's investment amount is 2 × php 20,000 = php 40,000
What is the probability that the sample proportion is greater than .43?
Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
Calculate probability ?
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.Probability and odds are two distinct ideas.Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. Theoretical Probability is one of three main categories of probability.Scientific Probability.Probability axiomatically. Sampling is frequently used to calculate the percentage of a population that possesses a particular attribute, such as the percentage of all defective goods that come off an assembly line or the percentage of all customers who enter a store and make a purchase before leaving.The proportions of the population and sample are represented by the letters p and p, respectively.
Therefore,
p = 0.43
if, in fact, 43% of shoppers make a purchase before leaving a store;
p = 78/200
= 0.39
if, in a sample of 200 shoppers, 78 make a purchase.
The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.
It will be represented as a random variable by the letter P.
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What’s the term for 5 _ 13
The nth term for the given series is given by 4n-3.
What is meant by series?
The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, but a sequence is an ordered collection of elements for which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression. A series can be finite or infinite in length and has a length that corresponds to the number of terms.The number series is 1, 5, 9, 13, 17,...
Common deviation (d)=5-1=4
A=1 is the first phrase.
A+(n1)d=1+(n1) is the formula for the nth term.
4=4n−3
∴tn =4n−3
The nth term for the given series is given by 4n-3.
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What percentage of this shape is shaded?
Answer:
Answer:
Step-by-step explanation:
There are 9 squares filled halfway, and 5 squares filled completely.
9 x 0.5 = 4.5
4.5 + 5 = 9.5
There are 25 squares in the shape.
9.5 / 25 = 0.38
38% of the square is shaded.
Four pencils held together with a band
Step-by-step explanation:
The length of the band is the number of units it covers
The actual length of the band is: \mathbf{40 + 10\pi}40+10π
The diameter of 1 pencil is given as:
\mathbf{d = 10}d=10
The circumference of 1 pencil is:
\mathbf{C = \pi d}C=πd
So, we have:
\mathbf{C = 10\pi }C=10π
Multiply by 4, to calculate the circumference of all pencils
\mathbf{4C =4 \times 10\pi }4C=4×10π
\mathbf{4C =40\pi }4C=40π
The rubber band covers a quarter of the 4 pencils.
So, we divide by 4
\mathbf{C = 10\pi }C=10π
The length of the band on one pencil is:
\mathbf{L = 10}L=10
Multiply by 4, for the 4 pencils
\mathbf{L = 40}L=40
So, the actual length of the band is:
\mathbf{Length = 40 + 10\pi}Length=40+10π
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Which value does NOT represent the shaded portion of the model shown? A 3/5 B. 0.3 C. 60% D. 0.6
Answer:
B
Step-by-step explanation:
All the rest = 3/5, 3 shaded out of 5
:]
Which point would describe the rate of change for the line modeled by y = 4/3x+2?
A. Vertical change of 2 units for each horizontal change of 1 unit
B. Vertical change of 1 unit for each horizontal change of 2 units
C. Vertical change of 4 units for each horizontal change of 3 units
D. Horizontal change of 4 units for each horizontal change of 3 units
The point which describe the rate of change for the line modeled by y = 4/3x+2 would be; C. Vertical change of 4 units for each horizontal change of 3 units
How to find the rate of change of a linear equation?Suppose that the considered linear equation is of the form y=mx+c
Then, when we change x by 1 unit, then:
[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]
where [tex]\delta y[/tex] shows the change in y as x changes by 1 unit.
It is found that this change is the value of 'm' called slope of the line this equation represents (each linear equation represents a line).
We have been given that the line modeled by y = 4/3x+2
The slope is given as m = 4/3
The point which describe the rate of change for the line modeled by y = 4/3x+2 would be;
C. Vertical change of 4 units for each horizontal change of 3 units
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46 over48 Are the ratios and proportional? 69 over 84 (1 point) A Yes, because they both reduce to the equivalent fraction 1 3 B Yes, because the cross products 46 84 and 48.69 are equal. C No, because one has a quotient of 06 and the other has a quotient of 0.571428- 2 D No, because one ratio reduces to 3 3 7 2 and the other reduces to
The ratios aren't proportional as D. No, because one ratio reduces to different values.
What is a ratio?A ratio is simply used to show the comparison between the numbers that are illustrated in a data.
In this case, the fractions that are given include 46/48 and 69/84.
To have an equivalent ratio, it's important to have the numerator and the denominator divided by the same number.
In this case, this isn't possible with 46/48 and 69/84.
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Justin has nine fudge popsicles.
He sells two popsicles to Sidney and three to Doryin.
What fraction of popsicles does Justin have left to eat?
Justin has sold 5 popsicles so from the original 9 if we take away 5, he has 4 popsicles left to eat.
9+x=11 what is the value of x?
Answer: the answer to that problem is
X=2
Match each problem to its solution.32672.72671.7216Jeff wants to buy a new guitar that costs$1,701.04. Currently, he has 51,029.32How many more dollars does he need tobuy the guitar?Rose walks 3.2 miles every day. How manymiles will she have walked in 5 days?Christie was on a road trip. She traveled320.95 miles on day one, 231.45 miles onday two, and 120.32 miles on day three.How many miles did she travel duringher three-day trip?Hugh drove 774.4 miles. His car averaged24.2 miles per gallon of gas. How manygallons of gas did the car use?No
Rose walks 3.2 miles every day. How many miles will she have walked in 5 days?
3.2*5 = 16 miles
Christie was on a road trip. She travelled 320.95 miles on day one, 231.45 miles on day two, and 120.32 miles on day three. How many miles did she travel during her three-day trip?
320.95 + 231.45 + 120.32 = 672.72 miles
Hugh drove 774.4 miles. His car averaged 24.2 miles per gallon of gas. How many gallons of gas did the car use?
774.4/24.2 = 32 gallons