The y-intercept in the first scenario represents the estimated stretching time if no jogging is done. In the second situation, the line of best fit equation shows that for each additional hour of jogging, an extra half minute of stretching is estimated. In the third scenario, Karen is predicted to sell about 12 cakes on her tenth week of operation.
The subject of this question is mathematics, specifically the concept of scatter plots and the line of best fit in linear regression. In the first scenario, the y-intercept of the line of best fit is 1 minute, which represents the estimated amount of time a student would spend stretching if they did not jog at all.
In the second scenario, the equation of the line of best fit is y = 0.5x + 1. This equation represents a relationship between the number of hours spent jogging (x) and the estimated minutes of stretching (y), where for every one extra hour of jogging, it is estimated that an additional half a minute is spent stretching.
Lastly, in the third scenario, using the line of best fit, Karen will likely sell approximately 12 cakes because the line of best fit is approximately y = 1x + 2, and substituting 10 for x (10th week), we get 12 (cakes).
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Solve the system of equations y = 40x2 and y = 19x + 3 algebraically.
We have been given a system of nonlinear equations.
[tex]\\y=40x^{2},y=19x+3[/tex]
In order to solve this system we can first equate the two equations in order to get a quadratic in x.
[tex]\\40x^{2}=19x+3[/tex]
Our next step is to bring all the terms on one side.
[tex]\\40x^{2}-19x-3=0[/tex]
Now we have to solve this equation. We can solve it by factoring using the splitting middle term method.
[tex]\\40x^{2}-24x+5x-3=0[/tex]
[tex]\\8x(5x-3)+(5x-3)=0[/tex]
[tex]\\(8x+1)(5x-3)=0[/tex]
Upon setting each of these factors equal to zero using zero product property we get
[tex]\\8x+1=0 \text{ or } 5x-3 = 0[/tex]
Upon solving both these equations we get
[tex]\\x=-\frac{1}{8} \text{ or } x=\frac{3}{5}[/tex]
Now we can substitute these values of x in the equation
[tex]y=19x+3[/tex]
We get
[tex]\text{For }x=- \frac{1}{8} \Rightarrow y=19(- \frac{1}{8})+3= \frac{5}{8}\\[/tex]
[tex]\text{For }x= \frac{3}{5}\Rightarrow y=19( \frac{3}{5})+3= \frac{72}{5}\\[/tex]
Therefore, our final set of solutions are
[tex](x,y)=(- \frac{1}{8},\frac{5}{8}) \text{ and } ( \frac{3}{5}, \frac{72}{5})[/tex]
A tank holds 1,000 gallons of syrup. Danielle filled 65 5-gallon cans with syrup. How much syrup was left in the tank when she finished? 3. Draw a picture or a chart that shows the information and the question.
675 gallons
935 gallons
325 gallons
350 gallons
Answer:
the answer is 675
Step-by-step explanation:
1. there is a tank with 1000 gallons, and we have 65 cans with a capacity of 5 gallons, so if we multiply the 65 cans with the capacity we would have as result
65 x 5 = 325
2- already having the value of gallons used (325) we can subtract this difference to the 1000 gallons that were in the tank at first.
1000 - 325 = 675
This is Josh’s solution for the equation
x2-6x-7=0:
x2-6x-7=0
x2-6x=7
x2-6x+9=7+9
(x-3)2=16
x=19
x-3=-16
x=-13
Is Josh’s solution correct? Explain
Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, space, c, m. He wanted his balloon to be bigger, so he blew 222 big breaths of air into the balloon. Each big breath increased the balloon's radius by 1 \text{ cm}1 cm1, space, c, m. What is the ratio of the current volume of the balloon to the original volume of the balloon?
Answer:
8 times
Step-by-step explanation:
I found the volume of the sphere. Then increased it how many times he blew. That was the ratio.
Also, Khan :)
The ratio of the current volume of the balloon to the original volume of the balloon is 8.
What is the volume of a sphere?The volume of a sphere is given by (4\3)πr³ where r is the radius of the sphere.
The initial volume of the balloon = [tex]\frac{4}{3} \pi 2^{3}[/tex]
The initial volume of the balloon =[tex]\frac{32}{3} \pi[/tex]
Radius of the balloon after first breath = 2+1 =3cm
The Radius of the balloon after the second breath = 2+2=4cm
So, the new volume of the balloon = [tex]\frac{4}{3} \pi 4^{3}[/tex]
The new volume of the balloon = [tex]\frac{256}{3} \pi[/tex]
The ratio of new volume to the initial volume = [tex]\frac{\frac{256}{3 } \pi }{\frac{32}{3}\pi }[/tex]
The ratio of new volume to the initial volume =8
Hence, the ratio of the current volume of the balloon to the original volume of the balloon is 8.
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What is the degree of the polynomial function f(x) = 2x3 + 7x5 − 4x − 12?
What is the volume of the coffee in a can if the can has a radius of 4 inches and a height of 9 inches? (use 3.14 for π.) 113.04 in.3 226.08 in.3 339.12 in.3 452.16 in.3?
The volume of the coffee in the can if the can has a radius of 4 inches and height of 9 inches is 452.16 inches³.
The can must be in the shape of a cylinder.
The formula to find the volume of the cylinder is,
Volume of cylinder = π r² h
Here r is the radius of the base of the cylinder and h is the height of the cylinder.
Given, Radius, r = 4 inches and Height, h = 9 inches
Volume of the coffee = π (4)² (9)
= 144 π
= 144 × 3.14
= 452.16 inches³
Thus, the volume of the coffee in the can is 452.16 inches³.
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please help will give brainiest!!!
NEED HELPPPPPPP!!!!!!! PLEASE!!!!!!!!
Which statement best describes the graph of -x3 - x2 + 4x + 4?
A. It starts down on the left and goes up on the right and intersects the axis at x = -2, 2, and 4.
B.It starts down on the left and goes up on the right and intersects the axis at x = -2, -1, and 2.
C.It starts up on the left and goes down on the right and intersects the x-axis at x = -2, -1, and 2.
D.It starts up on the left and goes down on the right and intersects the axis at x = -2, 2, and 4.
Firstly, simplife the function [tex] -x^3-x^2+4x+4 [/tex] in the following way:
[tex] -x^3-x^2+4x+4=-(x^3+x^2)+4(x+1)=-x^2(x+1)+4(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=-(x+2)(x+1)(x-2) [/tex].
There are three x-intercepts: x=-1; x=2 and x=-2 (therefore, options A and D are incorrect).
Since before brackets is sign "-", you should state that graph starts down on the left (you can check this substituting smaller negative number than -2 into function expression. For example, if x=-10, then f(-10)=-(-10+2)(-10+1)(-10-2)=-(-8)(-9)(-12)>0) and goes up on the right (you can check this substituting greater positive number than 2 into function expression. For example, if x=10, then f(-10)=-(10+2)(10+1)(10-2)=-(12)(11)(8)<0).
Answer: correct choice is B.
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. How many oranges are in the pile?
A.504 B.840 C.140 D.120
Answer:
Option C. 140
Step-by-step explanation:
Base of a pyramid which has four triangular sides is four sided.
If pyramid contains seven layers of oranges then the layer at the bottom will have 7 oranges.
Since base is a square then other side of the square base will have the same number of oranges = 7.
Therefore number of oranges at the first layer will be = 7×7
Similarly other layers above this layer will have the same sequence
6×6, 5×5, 4×4, 3×3, 2×2, 1×1
Therefore total number of oranges = 7×7 + 6×6 + 5×5 + 4×4 + 3×3 + 2×2 + 1×1 = 49 + 36 + 25 + 16 + 9 + 4 + 1 = 140
Option C. 140 is the answer.
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. Many oranges are in the pile are C.140
Further explanationThe orange is the fruit of the citrus species Citrus and sinensis in the family Rutaceae, native to China. Orange is also called sweet orange, to distinguish it from the related Citrus and aurantium, referred to as bitter orange.
The proper name of four-sided pyramid is a "tetrahedron". The tetrahedron has the extra interesting property of having all four triangular sides congruent
1st Layer: The 1st layer contains only 1 orange so it has only 1 orange
2nd layer: The 2nd layer has total 4 oranges. Calculation: [tex]2*2=4[/tex]
3rd layer: The 3rd layer has total 9 oranges. Calculation: [tex]3 * 3 = 9[/tex]
4th Layer: The 4th layer has total 16 oranges. Calculation: [tex]4 * 4 = 16[/tex].
5th layer: The 5th layer has total 25 oranges. Calculation: [tex]5 * 5 = 25[/tex]
6th layer: The 6th layer has total 36 oranges. Calculation: [tex]6 * 6 = 36[/tex]
7th layer: The 7th layer has total 49 oranges. Calculation: [tex]7 * 7 = 49[/tex].
Sum of all layers:
[tex]1+4+9+16+25+36+49 = 140[/tex]
Learn moreLearn more about oranges https://brainly.com/question/10744522Learn more about pyramid https://brainly.com/question/10262815Learn more about pile https://brainly.com/question/9094265Answer detailsGrade: 9
Subject: mathematics
Chapter: pyramid
Keywords: oranges, pyramid, four-sided, layers, pile
A plane intersects one cone of a double-napped cone such that the plane is neither parallel to the generating line nor perpendicular to the axis. What conic section is formed?
circle
hyperbola
ellipse
parabola
Area of figure? Geometry help???
A sample of 16 from a population produced a mean of 85.4 and a standard deviation of 14.8. a sample of 18 from another population produced a mean of 74.9 and a standard deviation of 16.0. assume that the two populations are normally distributed and the standard deviations of the two populations are equal. the null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is different than the mean of the second population. the significance level is 1%.
Solution: The test statistic under the null hypothesis is:
[tex]t=\frac{\bar{x_{1}}-\bar{x_{2}}}{s_{p}\sqrt{(\frac{1}{n_{1}})+(\frac{1}{n_{2}})}}[/tex]
Where:
[tex]s_{p} = \sqrt{\frac{(n_{1}-1)s^{2}_{1}+(n_{2}-1)s^{2}_{2}}{n_{1}+n_{2}-2} }[/tex]
[tex]s_{p} = \sqrt{\frac{(16-1)14.8^{2}+(18-1)16^{2}}{16+18-2} }[/tex]
[tex]=15.45[/tex]
[tex]\therefore t=\frac{85.4-74.9}{15.45\sqrt{(\frac{1}{16})+(\frac{1}{18})}}[/tex]
[tex]=\frac{10.5}{5.31}[/tex]
[tex]=1.98[/tex]
Now, to find the critical values, we need to use the t distribution table at 0.01 significance level for [tex]df=n_{1} + n_{2} -2 = 16+18-2=32[/tex] and is given below:
[tex]t_{critical}=-2.738,2.738[/tex]
Since the t statistic is less than the t critical value, we therefore fail to reject the null hypothesis and conclude that the two population means are equal.
How do do a 3/4 as a fraction, decimal, and percent?
Answer:
3/40.7575%Step-by-step explanation:
How do do a 3/4 as a fraction, decimal, and percent?
1) 3/4 is just a fraction
2) 3:4 = 0.75 (0.75 = 75%)
3) 75%
A sphere has a radius of 12 meters. What is the approximate volume of the sphere? Use 3.14 for π . Round your answer to the nearest whole number.
Pleaseee helpppp!!!!!!!!!!!!!!!!
Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth.
20, 16, 18, 9, 20, 16,14
A. mean=15.9 standard deviation= 3.6
B. mean= 16 standard deviation= 12.7
C. mean= 16.1 standard deviation= 3.6
D. mean= 16.1 standard deviation= 12.7
There are five apples and you take three away. how many apples do you have?
Answer: 2 apples
Step-by-step explanation:
Logic
Rafael has ridden 14 miles of a bike course. The course is 40 miles long. What percentage of the course has Rafael ridden so far
A bag contains a variety of different-colored marbles. If P(red) = , P(green) = , and P(red and green) = , which statement is true?
Answer:
The answer is A. The events are independent because P(red) • P(green) = P(red and green).
Answer:
A. The events are independent because P(red) • P(green) = P(red and green).
Step-by-step explanation:
EDGE 2021 AQR
The three undefined terms in geometry are point , line, and plane. True or false
What are the x intercepts of this function f(x) =2x^2-7x-4?
There are 25 counters is a bag 6 red, 4 white, 7 blue, and 8 yellow. you choose one counter at random. which color you least likely to choose
By calculating the probability of choosing a counter at random, we find that we are least likely to choose a white counter as it has the least probability.
What is probability?Probability is simply how likely something is to happen.
Probability of choosing a red counter = 6/25 = 0.24
Probability of choosing a white counter = 4/25 = 0.16
Probability of choosing a blue counter = 7/25 = 0.28
Probability of choosing a yellow counter = 8/25 = 0.32
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A jar contains 133 pennies.A bigger jar contains 1 2/7 times as many.What is the value of the pennies in the bigger jar?
Classify each polynomial by its degree and number of terms
Answer with explanation:
We know that a polynomial is classified based on the degree as follows:
Constant-
If it has a degree zero.
and the equation of such a polynomial is:
p(x)=a
Linear--
It has degree 1.
and the equation of such a polynomial is: p(x)=ax+b
Quadratic--
If it has degree two and the equation of the polynomial is given by:
[tex]p(x)=ax^2+bx+c[/tex]
Based on number of Terms--
Monomial--
If it has just one term.
Binomial--
If it has two terms.
Trinomial--
If it has three terms.
Given that the values in the table represent the graph of a continuous function, y has at least how many zeros? HELLLLP!!!!!!!!!
∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 72° and minor arc CD = 132°, what is the measure of ∠ABD?
A) 30°
B) 36°
C) 42°
D) 48°
Answer:
c 42 degrees
Step-by-step explanation:
Which accurately shows how to use inverse operations to find the value of a in a + 5 = 14?
Write the partial fraction decomposition of the given rational expression. startfraction 5 x plus 2 over x superscript 4 baseline minus 4 x squared endfraction
Answer:
Step-by-step explanation:
Given is a rational algebraic expression in x as
[tex]\frac{5x+2}{x^4-4x^2}[/tex]
First let us factorize the denominator.
[tex]x^2(x^2-4)\\=x^2(x+2)(x-2)[/tex]
Let the given term be
[tex]\frac{A}{x} +\frac{B}{x^2} +\frac{C}{x-2} +\frac{c}{x+2} \\\\=\frac{Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)}{x^4-4x^2}[/tex]
Equate the numerator to get
[tex]Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)[/tex]=[tex]5x+2[/tex]
Substitute x =-2
[tex]4D (-4) = -8\\D=\frac{1}{2}[/tex]
Now substitute x =2
We get
[tex]16C=12\\C=\frac{3}{4}[/tex]
Put x=0
[tex]-4B=2\\B=\frac{-1}{2}[/tex]
Next equate X cube terms to 0 on right side
[tex]A+C+D=0\\A=\frac{-5}{4}[/tex]
Hence partial fraction is
[tex]\frac{-1}{2x^2} -\frac{5}{4x} +\frac{1}{2(x+2)} +\frac{3}{4(x-2)}[/tex]
To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
Explanation:To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The denominator can be factored as x2(x2 - 4) which gives us two distinct linear factors x and x + 2, and a repeated linear factor x - 2. Therefore, we can express the rational expression as follows: startfraction A over x + B over x2 + C over (x - 2)2.
To find the values of A, B, and C, we can use the method of equating coefficients. By multiplying both sides of the equation by the common denominator, we can eliminate the fractions and solve for the unknowns. Finally, we substitute the values of A, B, and C back into the partial fraction decomposition expression.
Therefore, the partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
If BC is tangent to circle O and OB is a radius, what kind of triangle is OBC?
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 3 - 4 sin θ
Answer:
y-axis... just look at the graph on desmos.com