Given:
[tex]y=6x-4[/tex]Substitute the point (-3,-14)
[tex]\begin{gathered} -14=6(-3)-4 \\ -14=-18-4 \\ -14\ne-22 \end{gathered}[/tex]Substitute the point (3,14)
[tex]\begin{gathered} 14=6(3)-4 \\ 14=18-4 \\ 14=14 \end{gathered}[/tex]Substitute the point (-2,-16)
[tex]\begin{gathered} -16=6(-2)-4 \\ -16=-12-4 \\ -16=-16 \end{gathered}[/tex]Substitute (0,-4)
[tex]\begin{gathered} -4=6(0)-4 \\ -4=-4 \end{gathered}[/tex]Substitute (-2,16)
[tex]\begin{gathered} 16=6(-2)-4 \\ 16\ne-16 \end{gathered}[/tex]Points (3,14),(-2,-16) and (0,-4) are the solutions of the equation.
4. To check their accuracy, the Census Bureau draws a sample of several city blocks and recounts everyone in those blocks. What kind of sampling does this represent?Simple random samplingConvenience samplingSystematic samplingStratified samplingCluster sampling
In cluster sampling, the population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random. Therefore, in this case, the sampling represents a cluster sampling.
Answer: cluster sampling
How is the product of 3 x 1/4 related to the product of 3 x 1/2? Try to explain without finding the product. Use an array diagram to show how you know.
Ok, so
Let me draw an array diagram
Notice what, we will multiply 3 squares, per 1 square in a row.
Now, notice that if we draw the other array diagram:
If we analyze, we conclude that 3*(1/4) is exactly the half of 3/2.
below is a table with estimates of would population since 1AD
Answer:
1)
[tex]P(t)=1633e^{0.0087t}[/tex]Explanation:
Since we are taking t = 0 as 1900. The initial population is the population in 1900:
[tex]P_0=1633[/tex]We can start writting the exponential model:
[tex]P(t)=1633e^{kt}[/tex]:
We know that the population in 1950 (t = 50 in this model) is 2525. Then, we can find k by:
[tex]P(50)=2525=1633e^{k\cdot50}[/tex]And solve for k:
[tex]\frac{2525}{1633}=e^{50k}[/tex]Now, we can apply natural logarithm on both sides:
[tex]\ln(\frac{2525}{1633})=\ln(e^{50k})[/tex]Since natural log and the exponential functions are inverse functions:
[tex]\ln(\frac{2525}{1633})=50k[/tex][tex]k=\frac{\ln(\frac{2525}{1633})}{50}[/tex][tex]k\approx0.0087[/tex]Thus, the exponential model is:
[tex]P(t)=1633e^{0.0087t}[/tex] Question 2Now, we need to use the model we just create to find the predicted population by the model:
At year 1900, t = 0 (that's how the problem asked us to define t)
Then
[tex]P\left(0\right)=1633e^{0.0087\cdot0}=1633e^0=1633[/tex]At year 1920, t = 20
[tex]P(20)=1633e^{0.0087\cdot20}=1633e^{0.174}=1943[/tex]At year 1940, t = 40:
[tex]P(40)=1633e^{0.0087\cdot40}=1633e^{0.348}=2313[/tex]At year 1960, t = 60
[tex]P(60)=1633e^{0.0087\cdot60}=1633e^{0.522}=2752[/tex]At year 1980, t = 80
[tex]P(80)=1633e^{0.0087\cdot80}=1633e^{0.696}=3275[/tex]At year 2000, t = 100
[tex]P(100)=1633e^{0.0087\cdot100}=1633e^{0.87}=3898[/tex]At year 2020, t = 120
[tex]P(120)=1633e^{0.0087\cdot120}=1633e^{1.044}=4639[/tex]At year 2040, t = 140
[tex]P(140)=1633e^{0.0087\cdot140}=1633e^{1.218}=5520[/tex]GroupClare buys an item with a normal price of $24, butsaves $6 by using a coupon. For what percentage offis this coupon?
We are given the normal price as 24, but the discount amount is 6. This means the amount she saved, which is 6, represents the percentage off the normal price. Therefore, we can express this as follows;
[tex]\begin{gathered} \text{Percentage}=\frac{\text{discount amount}}{actual\text{ amount}}\times100 \\ \text{percentage}=\frac{6}{24}\times100 \\ \text{Percentage}=25 \end{gathered}[/tex]This means the coupon she used was for a 25% off the normal price
Statistics. Hi! I need the answer for this:The latest math quiz had an average score of 83.2 with a standard deviation of 3.4. What percent of students scored between a 79.8 and 86.6?
Answer:
[tex]68.27\text{ \%}[/tex]Explanation:
Here, we want to get the percentage of students that scored between the two scores
To get this, we need the z-scores of the given scores
Mathematically, we can calculate the z-scores as follows:
[tex]\begin{gathered} z\text{ = }\frac{x-\mu}{\sigma} \\ \\ \mu\text{ = mean = 83.2} \\ \sigma\text{ = standard deviation = 3.4} \end{gathered}[/tex]Now, we calculate the z-score for each of the scores. We call the first z1 and the second z2
We proceed as follows:
[tex]z_1=\frac{79.8-83.2}{3.4}\text{ = -1}[/tex]For the second score, we have:
[tex]z_2\text{ = }\frac{86.6-83.2}{3.4}\text{ = 1}[/tex]Finally, what we have to do is to find the probability between the two z-scores
We have this as follows:
[tex]P\mleft(-1The values of the z-score are obtained from the probability distribution tableThe mapping diagram shows a function R(x).910111289Which mapping diagram shows the inverse of R(x)?O A.DOO VO6789INB.9101112AAA89c!1211→10989O D.9101112→ 8→ 7
Since we want to find the values of the inverse function, we have to change the values of x for y values.
x r(x)
6 9
7 10
8 11
9 12
Changing x for y we have.
r'(x) x
6 9
7 10
8 11
9 12
The table below summarizes the amount of milk consumed by a sample of 27 families last month.Number of families Number of gallonsper familyFor these families, what is the mean number of gallons of milk consumed? Round your answer to the nearest tenth.gallons
There are 7 families with 1 gallon, 10 with 4 gallons and 10 with 5 gallons, so:
[tex]mean=\frac{7\cdot1+10\cdot4+10\cdot5}{27}[/tex][tex]mean=\frac{7+40+50}{27}[/tex][tex]mean=\frac{97}{27}\approx3.6\text{ gallons/family}[/tex]I just paid $29 membership and I cant asked a question, why?Question 5. The date death for a widow was 2017. If the estate was valued at $7.5 million and the estate was taxed at 40 percent, what was the heir's tax liability?
We need to use the formula for the taxable estate:
taxable estate= Estate value - exemption
Where the estate value is $7.5 million
and the exemption per state tax rule of 2017 is given by $5.490 million.
Then:
Taxable estate=$7.5 million - 5.5.490 million.
Taxable estate= 2.0.10.000
Finally, to find heir's tax liability, we need to multiply the taxable estate by the taxed percent.
Then:
heir's tax liability = 2.010.000*40%
heir's tax liability = 2.010.000*0.4
heir's tax liability = 804.000
Hence, the result is $ 804.000.
URGENTTTTT!!!!!!!Jennifer’s bank account is modeled by the following equation where x equals the number of weeks andf(x) equals the total balance.f(x) = 12x + 45william's bank account balances after weekly deposits are showing in the following table.How much money was in Jennifer's account when it was opened?Explain.
Jennifer’s bank account is modeled by the following equation where x equals the number of weeks and
f(x) equals the total balance.
f(x) = 12x + 45
william's bank account balances after weekly deposits are showing in the following table.
How much money was in Jennifer's account when it was opened?Explain.
Solution
For this case we can see that the amount starting for Jennifer is:
f(0)= 12(0) +45= 45
A rectangular room is 1.8 times as long as it is wide, and its perimeter is 35 meters.
Find the dimensions of the room. Round the answer to 2 decimal places.
Step-by-step explanation:
length = 1.8×width
2×length + 2×width = 35
now we use the first equation in the second :
2×(1.8×width) + 2×width = 35
3.6×width + 2×width = 35
5.6×width = 35
width = 35/5.6 = 6.25 meters
length = 1.8×width = 1.8×6.25 = 11.25 meters
A child needs to take 2 1/2 tablespoons of medicine per day in 8 equal doses. How much medicine is in each dose?
Given data:
The given medicine is 2 1/2= 2.5 tablesppons.
The numbers of doses are n=8.
The given expression can be written as,
8 doses=2.5 table spoon
1 dose =(2.5/8) table spoon
=0.3125 table spoon.
Thus, the medicine in one dose is 0.3125 table spoon.
plot the points listed below ok the same coordinate plane. describe any pattern you see in the graph (-3,-6), (-2,-5), (-1, -4)(0, -3)(1, -2)(2,-1)
From left to right, there are the corresponding pairs (-3,-6), (-2,-5), (-1, -4), (0, -3)(1, -2),(2,-1). The pattern is a line. This is the graph of a line.
Find the solution for the system of linear equations-x + y = 2 and 2x + y = -4
Answer:
[tex]\begin{gathered} x=-2 \\ y=0 \end{gathered}[/tex]Step-by-step explanation:
Given the system of equations:
[tex]\begin{cases}-x+y=2 \\ 2x+y=-4\end{cases}[/tex]We'll multiply the first equation by 2:
[tex]\begin{cases}-x+y=2 \\ 2x+y=-4\end{cases}\rightarrow\begin{cases}-2x+2y=4 \\ 2x+y=-4\end{cases}[/tex]Then, we'll add up both equations and solve for y, as following:
[tex]\begin{cases}-2x+2y=4 \\ 2x+y=-4\end{cases}\rightarrow3y=0\rightarrow y=0[/tex]Now, we'll plug in this y-value in the second equation and solve for x, as following:
[tex]\begin{gathered} 2x+y=-4 \\ \rightarrow2x+0=-4 \\ \rightarrow2x=-4 \\ \\ \Rightarrow x=-2 \end{gathered}[/tex]This way, we'll have that the solution to the system of linear equations is:
[tex]\begin{gathered} x=-2 \\ y=0 \end{gathered}[/tex]Create a function that models the table of values (Please help)
Examining the table the function that models the table of values is
f ( x ) = 2x^2 - 1
How to determine the function that models the table of valuesThe table represents functions of input variables and the output variables.
The function that models the table of values will be in such a way that the function represents the relationship between the input and out variables
comparing the values and the function
f ( x ) = 2x^2 - 1
at x = 0 ⇒ f ( 0 ) = 2 * (0)^2 - 1 = - 1
at x = 1 ⇒ f ( 1 ) = 2 * (1)^2 - 1 = 1
at x = 2 ⇒ f ( 2 ) = 2 * (2)^2 - 1 = 7
This shows that f ( x ) = 2x^2 - 1 is the function that models the table of value
Learn more on function that models the table of value at :
https://brainly.com/question/29216888
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solve the inequality. show your work and remember to switch the symbol.
PROBLEM
Inequalities
Method
When solving linear inequalities, change or switch the sign of the inequality when you divide or multiple with negative.
[tex]\begin{gathered} - \\ -5b\text{ }\ge\text{ 20} \\ \text{Divide through by -5} \\ \frac{-5b}{-5}\text{ }\leq\text{ }\frac{20}{-5} \\ b\text{ }\leq\text{ -4} \end{gathered}[/tex]Can you check this problem for me please? Solve the following equation: - 3(x+4)=-5xThe answer I got was: X=6
Question:
Solve the following equation: - 3(x+4)=-5x
Solution:
Consider the following equation:
[tex]-3(x+4)=\text{ -5x}[/tex]This is equivalent to:
[tex]-3x\text{ -12 = -5x}[/tex]now, joining similar terms we get:
[tex]-3x\text{ + 5x = 12}[/tex]this is equivalent to:
[tex]2x\text{ = 12}[/tex]solving for x:
[tex]x\text{ = }\frac{12}{2}=\text{ 6}[/tex]then, we can conclude that the correct answer is:
[tex]x\text{ = 6}[/tex]Find the interest on the loan if Tim borrows $10,000 for 3 years at a simple interest of 10%
Simple interest formula:
[tex]I=P\times r\times t[/tex]I is the interest
P is the principal amount
r is the rate of interest in decimal form
t is the time in years
For the given situation:
P=10,000
r= (10/100)=0.1
t=3
[tex]\begin{gathered} I=10,000\times0.1\times3 \\ \\ I=3,000 \end{gathered}[/tex]Then, the interest on the loan is $3,000A right triangle has legs 15 and 14 inches. What is the measurement of the missing side?
For right triangles we can use the pythagoream theorem in order to calculate the length of missing sides, by means of the following formula:
[tex]undefined[/tex]A rectangular prism has volume 5,760 cubic meters, length 8 meters, and width 36 meters. Find its height, in meters.
The volume of a rectangular prism is given as:
[tex]V=lwh[/tex]where l is the length, w is the width and h is the height. Plugging the values given we have:
[tex]5760=8\cdot36\cdot h[/tex]Solving for h we have:
[tex]h=\frac{5760}{8\cdot36}=\frac{5760}{288}=20[/tex]Therefore the height is 20 meters.
The volume of the square pyramid is ___ cubic meters.
The volume of a pyramid is equal to one-third of the product of the base area and the height, following the formula:
[tex]V=\frac{1}{3}A_{\text{base}}\cdot h[/tex]Since the base of the pyramid is a square, the area of its base is equal to the square of its side length:
[tex]A_{\text{base}}=a^2[/tex]Then, you can write the formula for the volume as follows:
[tex]V=\frac{1}{3}a^2h[/tex]The side length of the base is a=30m and the height of the pyramid is h=20m, replace both values on the formula to calculate the volume:
[tex]\begin{gathered} V=\frac{1}{3}\cdot(30^2)\cdot20 \\ V=\frac{1}{3}\cdot900\cdot20 \\ V=\frac{1}{3}\cdot18000 \\ V=6000m^3 \end{gathered}[/tex]The volume of the square pyramid is 6000m³
What is the x intercept nd plot on the graph
Hello
To solve this question, we have to draw this graph
From the graph above, we can see that the intercept is at +4
what is 2+2 if you help i will give you nothing thanks
The given expression is,
[tex]2+2[/tex]By adding two with another two, we get, 4.
Thus,
[tex]2+2=4[/tex]Su needs 18/24 of a block of clay in order to make a bowl. Does she need to cut the whole block into 24 equal pieces?
it's not necessary to cut the block, she could divide the block into 24 equal parts and then take 18 parts of 24 parts.
what expression shows the amount of profit earned when 15 tuxedos are dry clean
The profit equation is given as,
p=x(20-(4+8h))
Here, x is the number of tuxedos.
Given, x=15
Substitute x= 15 in profit equation.
[tex]\begin{gathered} p=15(20-(4+8h) \\ p=15X20-15(4+8h) \\ p=300-15X4-15X8h \\ p=300-60-120h \\ p=240-120h \end{gathered}[/tex]Find the sum of the first 85 terms of the sequence –3, –1, 1, 3, …Select one:a.6804b.6887c.6885d.6881
Given:
The sequence is: -3, -1, 1, 3,..
Required: The sum of the first 85 terms
The sequence is a an arithmetic progression where:
first term (a) = -3
common difference (d) = 2
The formula for the sum of the first n terms of an arithmetic progression is:
[tex]S_n=\text{ }\frac{n}{2}[2a\text{ + \lparen n-1\rparen d\rbrack}[/tex]For this problem, n = 85
Substituting the given values:
[tex]\begin{gathered} S_{85}\text{ = }\frac{85}{2}[2\times-3\text{ + \lparen85-1\rparen}\times2] \\ =\text{ 6885} \end{gathered}[/tex]Answer: Option C
Check all that apply. Pie over 6 is the reference angle for:
π/6 is in quadrant I.
The reference angle of an angle in quadrat I is the same angle (If you add or subtract 2π to the angle n times you get the same angle).
Then, the reference angle or π/6 are:
[tex]\begin{gathered} \frac{\pi}{6} \\ \\ \frac{\pi}{6}+2\pi=\frac{\pi+12\pi}{6}=\frac{13\pi}{6} \\ \\ \frac{\pi}{6}+2(2\pi)=\frac{\pi}{6}+4\pi=\frac{\pi+24\pi}{6}=\frac{25\pi}{6} \\ \\ \frac{\pi}{6}-2\pi=\frac{\pi-12\pi}{6}=-\frac{11\pi}{6} \end{gathered}[/tex]For the given options just 13π/6 is a reference angle for π/6Answer: DWhich of the points satisfy the linear inequality graphed here A: 10,10B: 10,0C-10,0D: 0,0
Answer:
C (-10,0)
Explanation:
We need to find a point that lies in the blue r
write a word problem that can be represented by the expression 5/6 / 1/3
5/6 / 1/3
5/6 and 1/3 are fractions
Firstly, let us express this in ratio
Felix and Newton want to share apples in the ratio of 5 to 6 and also want to share marbles in the ratio of 1 to 3. Find the number of apples and marbles each of them will get?
To share apples in the ratio of 5 to 6
This means that felix will take 6 apples and Newton will have 6 apples and it become
5: 6= 5/6
Same thing applicable to the sharing of marbles
1 : 3 = 1/3
Answer:
There are a total of 5/6 pieces chocolates. each person wants ⅓ part of that, how many people will get ⅓.
-7 Locate the point (2,-2) on the coordinate plane: 12 / 2 3 N 1 -3 -2 -1 N 3 -1 -2 -3
The given point is (2, -2), which x = 2 and y = -2.
Remember that the positive numbers of x are on the right side of the axis, and the negative numbers of y are on the bottom part of the axis.
Hence, the located point would be
PO has endpoints at P(-5.4) and Q(7-5). What is the length of PQ?
Answer:
Explanation:
If line segments PQ has endpoints at P(-5, 4) and Q(7, -5).
To determine the length of the line, we use the distance formula:
[tex]\begin{gathered} Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Where:} \\ $$\mleft(x_1,y_1\mright)=P\mleft(-5,4\mright)$$ \\ (x_2,y_2)=Q\mleft(7,-5\mright). \end{gathered}[/tex]Substituting the given values, we have:
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