Answer:
26
Step-by-step explanation:
Just plug -3 in where ever you see x
[tex]f(x)=5-7x\\f(-3)=5-7(-3)\\f(-3)=5+21\\f(-3)=26[/tex]
p(x) = x + 4; Find p(2) evaluate function
Given:
The function is,
[tex]p(x)=x+4[/tex]Explanation:
Substitute 2 for x in the function to determine the value of p(2).
[tex]\begin{gathered} p(2)=2+4 \\ =6 \end{gathered}[/tex]So answer is p(2) = 6
Malachi is making a fruit smoothie. In addition to a frozen banana, he wants to add one other fruit and one small container of yogurt.
If he has four different options for fruit (blueberries, strawberries, peaches, and raspberries) and three different options for yogurt flavors (plain, vanilla, and lemon), how many fruit smoothie combinations are possible?
There are
possible fruit smoothie combinations.
Answer:
12 different combinations are possible (I think)
Step-by-step explanation:
Let's try to understand,
1. Blueberries + Plain Yogurt
2. Strawberries + Plain Yogurt
3. Peaches+ Plain Yogurt
4. Raspberries + Plain Yogurt
5. Blueberries + Vanilla Yogurt
6. Strawberries +VanillaYogurt
7. Peaches+ VanillaYogurt
8. Raspberries + VanillaYogurt
9. Blueberries + Lemon Yogurt
10. Strawberries + Lemon Yogurt
11. Peaches+ Lemon Yogurt
12. Raspberries + LemonYogurt
I hope this is the right answer and if not please forgive.
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.
ANSWER:
Separate the quotient in two terms
STEP-BY-STEP EXPLANATION:
We have the following:
[tex]\begin{gathered} \tan x=\frac{\sin x}{\cos x} \\ \tan x=\frac{1}{\cos x}\cdot\sin x \end{gathered}[/tex]Therefore, the step shown in the image is to separate the quotient in two terms
Danica made $319 babysitting last month in that might she babysitted for total of 29 hours how much money did Danica make per hour
Answer:
Explanation:
From the question, we are told that Danica
Help first one to get this correct will be marked
Answer:
1st one
Step-by-step explanation:
1st one
You have one input (x) with more than one output (y)
(-9, -9) and (-9, 6)
Determine the equation of the graphed circleReminder that the equation should look like the example I provided
The equation of a circle of radius r and center at (h, k) is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]The image provided shows a circle and we must find the radius and center by simple inspection.
The center is located at (-5, 3).
From that point, until I find a point of the circumference I can count 4 units. It is confirmed when I see the segment from (-9, 3) to (-1, 3) as a diameter of length 8. The radius is half the diameter, thus r = 4.
Substituting, we have the required equation:
[tex]\begin{gathered} (x+5)^2+(y-3)^2=4^2 \\ \boxed{\mleft(x+5\mright)^2+\mleft(y-3\mright)^2=16} \end{gathered}[/tex]The wholesale price for a bookcase is 152$. A certain furniture marks up the wholesale price by 36%. find the price of the bookcase in the furniture store. round answer by the nearest cent, as necessary
The price of the bookcase in the funiture store is:
$206.72
Explanation:Given that the markup is 36% of $152
This is:
0.36 * 152 = $54.72
Therefore, the price of the bookcase in the funiture store is:
$152 + $54.72
= $206.72
Answer the questions below about the quadratic function.g(×)=2×^2-12×+19Does the function have a minimum or maximum? minimum or maximum what is the functions minimum or maximum value?Where does the minimum or maximum value occur?x=?
Given the function:
[tex]g(x)=2x^2-12x+19[/tex]Let's determine if the function has a minimum or maximum.
The minimum and maximum of a function are the smallest and largest value of a function in a given range or domain
The given function has a minimum.
Apply the general equation of a quadratic function:
[tex]y=ax^2+bx+c[/tex]To find the minimum value, apply the formula:
[tex]x=-\frac{b}{2a}[/tex]Where:
b = -12
a = 2
Thus, we have:
[tex]\begin{gathered} x=-\frac{-12}{2(2)} \\ \\ x=-\frac{-12}{4} \\ \\ x=3 \end{gathered}[/tex]To find the function's minimum value, find f(3).
Substitute 3 for x in the function and evaluate:
[tex]\begin{gathered} f(x)=2x^2-12x+19 \\ \\ f(3)=2(3)^2-12(3)+19 \\ \\ f(3)=2(9)-36+19 \\ \\ f(3)=18-36+19 \\ \\ f(3)=1 \end{gathered}[/tex]Therefore, the function's minimum value is 1
Therefore, the functions minimum value occurs at:
x = 3
ANSWER:
• The function has a minimum
• Minimum value: 1
• The minimum occurs at: x = 3
19. The table below shows the population of Florida from 2010 to 2019.YearPopulation (millions)201018.7201119.1201219.3201319.6201419.9201520.2201620.6201721.0201821.2201921.5(a) Use a graphing calculator to build a logistic regression model that best fits this data, letting t=0 in 2010. Round each coefficient to two decimal places.Pt = (b) What does this model predict that the population of Florida will be in 2030? Round your answer to one decimal place. million people(c) When does this model predict that Florida's population will reach 23 million? Give your answer as a calendar year (ex: 2010).During the year (d) According to this model, what is the carrying capacity for Florida's population? million people
The formula for the logistic regression model that best fits the data is,
[tex]y_1=\frac{a}{1+b\cdot e^{t\cdot x_{1}}}[/tex]The graph, tables and details of the population data will be shown below
a) The equation that best fits the regression model is,
[tex]\begin{gathered} P_t=y_1 \\ t=x_1 \\ a=93.2861\approx93.29(2\text{ decimal places)} \\ b=3.98291\approx3.98(2\text{ decimal places)} \\ t=-0.0198742\approx-0.02(2\text{ decimal places)} \end{gathered}[/tex]Substitutes the data above into the equation
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]Hence,
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]b) In the year 2030, t = 20
[tex]\begin{gathered} P_{20}=\frac{93.29}{1+3.98\cdot e^{-0.02\times20}}=\frac{93.29}{1+3.98\cdot e^{-0.4}}=\frac{93.29}{1+3.98\times0.67032} \\ P_{20}=\frac{93.29}{1+2.6678736}=\frac{93.29}{3.6678736}=25.43435521\approx25.4(1\text{ decimal place)} \\ P_{20}=25.4million\text{ people} \end{gathered}[/tex]Hence, the answer is
[tex]P_{20}=25.4\text{million people}[/tex]c) Given that
[tex]\begin{gathered} _{}P_t=23\text{million people} \\ 23=\frac{93.29}{1+3.98\cdot e^{-0.02t}} \end{gathered}[/tex]Multiply both sides by 1+3.98e^{-0.02t}
[tex]\begin{gathered} 23(1+3.98e^{-0.02t})=1+3.98e^{-0.02t}\times\frac{93.29}{1+3.98\cdot e^{-0.02t}} \\ \frac{23(1+3.98e^{-0.02t})}{23}=\frac{93.29}{23} \\ 1+3.98e^{-0.02t}=4.056087 \end{gathered}[/tex]Subtract 1 from both sides
[tex]\begin{gathered} 1+3.98e^{-0.02t}-1=4.056087-1 \\ 3.98e^{-0.02t}=3.056087 \end{gathered}[/tex]Divide both sides by 3.98
[tex]\begin{gathered} \frac{3.98e^{-0.02t}}{3.98}=\frac{3.056087}{3.98} \\ e^{-0.02t}=0.767861055 \end{gathered}[/tex]Apply exponent rule
[tex]\begin{gathered} -0.02t=\ln 0.767861055 \\ -0.02t=-0.264146479 \end{gathered}[/tex]Divide both sides by -0.02
[tex]\begin{gathered} \frac{-0.02t}{-0.02}=\frac{-0.264146479}{-0.02} \\ t=13.20732\approx13(nearest\text{ whole number)} \\ t=13 \end{gathered}[/tex]Hence, the population will reach 23million in the year 2023.
d) The carrying capacity for Florida's population is equal to the value of a.
[tex]\begin{gathered} \text{where,} \\ a=93.29\text{ million people} \end{gathered}[/tex]Hence, the carrying capacity fof Florida's population is
[tex]93.29\text{million people}[/tex]
I would like to know how to solve this answer.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
k > 0
k * v
Step 02:
Scalars and Vectors:
k = scalar
v = vector
Scalar multiplication of a real vector by a positive real number multiplies the vector's magnitude, without changing its direction.
k * v
The answer is:
k v is parallel and has same direction as v
karen recorded her walking pace in the table below. what equation best represents this relationship
Given Data:
The table given here shows time taken in the first column and the distance travelled in the second column.
First check the ration of distance /time to verify if the speed of the man is constant or not.
[tex]\begin{gathered} \frac{8.75\text{ m}}{2.5\text{ h}}=3.5\text{ m/h} \\ \frac{14\text{ m}}{4\text{ h}}=3.5\text{ m/h} \end{gathered}[/tex]As both ratios are same it means the speed of the man is constant and the distance travelled is directly proportional to the time taken and varies linealy with the time.
Now to determine the relationship between m and h we will use the same ratio of m and h which comes in the previous step.
[tex]\begin{gathered} \frac{m}{h}=3.5 \\ m=3.5h \end{gathered}[/tex]Thus, option (D) is the required solution.
there are approximately 1.2 x 10^8 households in the U.S. If the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day ? Please Answer this im scientific notation
According to the given data we have the following:
total households in the US=1.2*10^8. hence:
[tex]1.2*10^8=120000000[/tex]average household uses 400 gallons of water each day
let x=total number of gallons of water used by households in the US each day
Therefore x=total households in the US*average gallons of water households uses each day
x=120,000,000*400
x=48,000,000,000
The total number of gallons of water used by households in the US each day is 48,000,000,000
The slope of the line containing the points (-2, 3) and (-3, 1) is
Hey :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Apply the little slope equation. By doing that successfully, we should get our correct slope.
[tex]\large\boldsymbol{\frac{y2-y1}{x2-x1}}[/tex]
[tex]\large\boldsymbol{\frac{1-3}{-3-(-2)}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-3+2}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-1}}[/tex]
[tex]\large\boldsymbol{-2}}[/tex]
So, the calculations showed that the slope is -2. I hope i could provide a good explanation and a correct answer to you. Thank you for taking the time to read my answer.
here for further service,
silennia[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2–8x+2
We have to calculate the zeros of the function with the quadratic formula.
[tex]f(x)=x^2-8x+2[/tex][tex]\begin{gathered} x=\frac{-(-8)}{2\cdot1}\pm\frac{\sqrt[]{(-8)^2-4\cdot1\cdot2}}{2\cdot1}=\frac{8}{2}\pm\frac{\sqrt[]{64-8}}{2}=4\pm\frac{\sqrt[]{56}}{2}=4\pm\sqrt[]{\frac{56}{4}}=4\pm\sqrt[]{14} \\ \\ x_1=4+\sqrt[]{14}\approx4+3.742=7.742 \\ x_2=4-\sqrt[]{14}\approx4-3.742=0.258 \end{gathered}[/tex]The roots are x1=7.742 and x2=0.258, both reals., both
In the expression 9+2z what is the variable?
To answer this question, we will define some things first.
For every mathematical expression or term, it consist of three parts:
1) Coefficient
2) Variable: a symbol that stands in for an unknown value in a mathematical expression
3) Constant
In the expression given:
[tex]\begin{gathered} 9+2z \\ 9\text{ is the constant} \\ 2\text{ is the coefficient} \\ z\text{ is the variable} \end{gathered}[/tex]So the variable in the expression is z.
3t^2-2t+5; find the company revenues last month if t=-1
Given revenue function is:
[tex]R=3t^2-2t+5[/tex]Now revenue at t=(-1)
[tex]\begin{gathered} R=3(-1)^2-2(-1)+5 \\ R=3+2+5 \\ R=10 \end{gathered}[/tex]So the revenue at t=-1 is 10.
Which number line shows the solutions to x > 5? O A. A. 3642 8 2 4 6 8 B. 8 -6 -4 -2 0 2 4 6 8 c. -6-4 2 0 2 4 6 8 D. 8 8 4 2 0 2 4 6 8
The answer is option C.
thats where there are intergers greater than 5.
Amelia used 6 liters of gasoline to drive 48 kilometers.How many kilometers did Amelia drive per liter?kilometers =At that rate, how many liters does it take to drive 1 kilometer?liters =
Answer:
8km /hr
1/ 8 of a litre.
Explanation:
We are told that Amelia drives 48 kilometres in 6 hours, this means the number of kilometres she drives per litre is
[tex]48\operatorname{km}\div6\text{litres}[/tex][tex]\frac{8\operatorname{km}}{\text{litre}}[/tex]Hence, Amelia drives 8 kilometres per litre.
The next question can be rephrased as, given that Amelia drives 8 km per litre, how many litres will it take to drive one kilometre?
To answer this question, we make use of the equation
[tex]\operatorname{km}\text{ travelled = 8km/litre }\cdot\text{ litres}[/tex]Now, we want
km travelled = 1 km
and the above equation gives
[tex]\begin{gathered} 1=\frac{8\operatorname{km}}{\text{litre}}\cdot\text{litres} \\ 1=8\cdot\text{litres} \end{gathered}[/tex]Dividing both sides by 8 gives
[tex]\text{litres}=\frac{1}{8}[/tex]Hence, it takes 1/8 of a litre to drive 1 kilometre.
A recipe uses 6 cups of flour to 1 1/10 cups of milk. If you have 2 cups of flour, how much milk should you use?
We were told that the recipe uses 6 cups of flour to 1 1/10 cups of milk. Converting 1 1/10 to improper fraction, it becomes 11/10
Let x represent the number of cups of milk that would be used for 2 cups of flour. The equations would be as shown below
11/10 = 6
x = 2
By cross multiplying, we have
2 * 11/10 = 6 * x
6x = 22/10 = 11/5
x = (11/5) / 6
If we flip 6 such that it becomes 1/6, the division sign changes to multiplication. Thus, we have
x = 11/5 * 1/6 = 11/30
Thus, 11/30 cup of milk should be used
How do you solve letter b using a subtraction equation with one variable that has a solution of 2/3. A step by step guide would be helpful.
Let's set x as the variable that has a solution of 2/3.
A possible equation is:
[tex]1-x=y[/tex]Now, in order to know the y-value, replace the x-value=2/3 and solve for y:
[tex]\begin{gathered} 1-\frac{2}{3}=y \\ we\text{ can replace 1 by 1/1} \\ \frac{1}{1}-\frac{2}{3}=y \\ \text{The subtraction of fractions can be solved as} \\ \frac{1\times3-1\times2}{1\times3}=y \\ \frac{3-2}{3}=y \\ \frac{1}{3}=y \end{gathered}[/tex]Now, replace the y-value in the initial equation, and we obtain:
[tex]1-x=\frac{1}{3}[/tex]If you solve this equation, you will get x=2/3.
Equation of the line that passes through points (8,7) and (0,0)
Equation of the line:
y = mx+b
where:
m= slope
b= y-intercept
First, we have to find the slope:
m = (y2-y1) / (x2-x1)
Since we have:
(x1,y1) = (8,7)
(x2,y2)= (0,0)
Replacing:
m = (0-7)/ (0-8) = -7/-8 = 7/8
Now, that we have the slope:
y = 7/8 x +b
We can place the point (8,7) in the equation and solve for b:
7 = 7/8 (8) +b
7=7 +b
7-7=b
b=0
Since the y-intercept=0
The final equation is:
y= 7/8x
New Orleans is 2 feet below sea level. Salton City has an elevation that is lower than New Orleans. What is a possible elevation, in feet, of Salton City?
Answer:
-4 feet (4 feet below sea level)
Salton City's potential elevation is determined to be 3 feet below sea level by using a number line and the elevation of New Orleans, which is 2 feet below sea level.
What is meant by number line?A number line is a mathematical visual representation of numbers on a straight line. On a number line, the numbers are arranged in order at regular intervals along its length.It often appears horizontally and could extend indefinitely in either direction. A number line is a horizontal line with consistently spaced numerical increments.How the number on the line can be answered depends on the numbers that are present. Given, the elevation indicates that New Orleans is 2 feet below (lower than) sea level.The elevation of Salton City is lower than that of New Orleans. Required; potential rise of Salton CitySalton City's elevation can be calculated using the information below on a number line: We have;& |t; |-3 |-2 |0 > if SL stands for sea level, N for New Orleans, and S for Salton City. On the number line above, a S. N. SLA point to the right of the -2 mark denotes an elevation that is higher than New Orleans, and a point to the left of -2 denotes an elevation that is lower than New Orleans.Therefore,
Salton City should be located to the left of -2, which is a point, at a distance of x -2 feet.
Salton City's elevation, which is determined by the set x -2 feet, is less than 2 feet above sea level.
Since -3 feet is less than -2 feet, Salton City's elevation might be as low as x = 3 feet below sea level, which is less than () 2 feet below sea level.
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(4, 2); slope = 3 writing linear equations given point and slope
The standard equation of a line in point-slope form is expressed as;
y-y0 = m(x-x0) where;
m is the slope
(x0, y0) is the point on the line
Given
(x0, y0) = (4, 2)
From the coordinate;
x0 = 4 and y0 =2
slope m = 3
Substitute the given parameters into the equation as shown;
y-2 = 3(x-4)
Hence the linear equations given the point and slope id expressed as y-2 = 3(x-4)
Find the length of the legs of a night triangle whose hypotenuse is 25cm and whose area is 84cm use phytagorean theorem.
Answer:
Explanation:
Here, we want to find the length of the legs of the right triangle given the area and the length of the hypotenuse
We have the sketch of the triangle as shown below:
According to Pythagoras' the square of the length of the hypotenuse equals the sum of the squares of the length of the two other sides
Thus, mathematically:
[tex]a^2\text{ + b}^2\text{ = 25}^2[/tex]Mathematically, we have the area calculated as:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times b\times h \\ \\ 84\text{ = }\frac{1}{2}\times a\times b \\ \\ a\text{ = }\frac{168}{b} \end{gathered}[/tex]Now, we have two equations to solve simultaneously
Substitute equation ii into i
We have that as:
[tex][/tex]Question 2 A recipe for homemade modeling clay requires 4 parts plain flour to 1 part cornstarch. Indicate whether each set of ingredients below is proportional to the recipe. Proportional Not Proportional 8 cups plain flour and 2 cups cornstarch 20 cups plain flour and 5 cups cornstarch 2 cups plain flour and 1 cup cornstarch Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Frequirements | Platform Status 2021 McGraw-HI Education. All Rights Reserved
The given ratio is 4 parts of plain flour to 1 part of cornstarch.
So, each recipe with the same ratio will be the answer.
As you can observe, the first choice is proportional because the plain flour is 4 times the cornstarch.
The second choice is proportional too because the plain flour is 4 times the cornstarch.
However, the last choice is not proportional because it has a ratio of double, which is not correct.
The data for numbers of times per week 20 students at Stackamole High eat vegetables are shown below. A dotplot shows 4 points above 1, 4 points above 3, 5 points above 2, 3 points above 4, 3 points above 5, and 1 point above 9.
Considering the given dot plot for the distribution, it is found that:
a) The distribution is right skewed.
b) There is an outlier at 9.
c) Since there is an outlier, the best measure of center is the median.
Dot plotA dot plot shows the number of times that each measure appears in the data-set, hence the data-set is given as follows:
1, 1, 1, 1, 2, 2, 2, 2, 2 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 9.
To find the skewness of the data-set, we need to find the mean and the median.
The mean is the sum of all values divided by the number of values of 20, hence:
Mean = (4 x 1 + 5 x 2 + 4 x 3 + 3 x 4 + 3 x 5 + 9)/20 = 3.1.
The median is the mean of the 9th and the 10th elements(even cardinality) of the data-set, hence:
Median = (2 + 3)/2 = 2.5.
The mean is greater than the median, hence the distribution is right skewed.
To identity outliers, we need to look at the quartiles, as follows:
First quartile: 0.25 x 20 = 5th element = 2.Third quartile: 0.75 x 20 = 15th element = 4.The interquartile range is:
IQR = 4 - 2 = 2.
Outliers are more than IQR from the quartiles, hence:
4 + 1.5 x 2 = 4 + 3 = 7 < 9, hence 9 is an outlier in the data-set, and hence the median will be the best measure of center.
Missing information
The questions are as follows:
Part A: Describe the dotplot. (4 points)
Part B: What, if any, are the outliers in these data? Show your work. (3 points)
Part C: What is the best measure of center for these data? Explain your reasoning. (3 points) (10 points)
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2/5m = 1/2 what is the m stand for ?
we can interpret m as a constant of proportionality.
The area of this figure 20 in. is square inches. 28 in. 30 in. 7 in. 25 in.
The shape can be broken into two separate rectangles of the forms below.
Bothe shapes give a rectangle, therefore the area of the shape is
Area of Shape = Area of rectangle A + Area of rectangle B
Since Area of rectangle = LENGTH X BREADTH, we then have below
[tex]\begin{gathered} \text{Area of shape = (28 x 7)}+(25\times30) \\ =196+750 \\ =946\text{ square inches} \end{gathered}[/tex]In conclusion, the answer is 946 square inches
Debra is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her unlocking the treasure chest is 3/10. Find the odds in favor of her character unlocking the treasure chest.
Probability of Debra unlocking the treasure chest, P(unlocking) = 3/10
Probability of Debra not unlocking the treasure chest,
P( not unlocking) = 1 - 3/10
P( not unlocking) = 7/10
[tex]undefined[/tex]The scatter plot shows the number of CDs in millions that were sold from 1999 to 2005. Use the points (1999,940) and (2002,805) to find a line of fit for the data. Then use the line of fit to estimate the number of CDs that were sold in 2008
Based on the given points from the scatter plot on the number of CDs sold in millions, the line of best fit for the data is y = -45x + 90,895
The estimated number of CDs sold in 2008 was 535 CDs.
How to find the line of best fit?The line of best fit will take the form:
y = Slope(x) + y intercept
The value of x will be assumed to be the number of years since 1999.
The slope is:
= Change in y / Change in x
= (805 - 940) / (2002 - 1999)
= -45
The y intercept is:
940 = -45(3) + y
y = 90,895
The line of best fit is:
y = -45x + 90,895
This means that the number of CDs sold in 2008:
= -45(2008) + 90,895
= 535 CDs
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