Answer:
12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft
Step-by-step explanation:
Given that truck can hold = 504 [tex]ft^{3}[/tex] i.e.
Volume, V = 504 [tex]ft^{3}[/tex]
Length of cargo space = 12 ft
Let width of cargo space = w ft
As per question statement:
Let height of cargo space = (w-1) ft
To find: The Dimensions of Cargo Space
Formula for Volume of Cargo Space:
V = Length [tex]\times[/tex] Width [tex]\times[/tex] Height
Putting the given values and conditions:
504 = 12 [tex]\times[/tex] [tex]w \times (w-1)[/tex]
[tex]\Rightarrow w(w-1) = \dfrac{504}{12}\\\Rightarrow w^{2} -w = 42\\\Rightarrow w^{2} -w - 42=0\\\Rightarrow w^{2} -7w +6w -42 =0\\\Rightarrow w(w -7) +6(w -7) =0\\\Rightarrow (w -7)(w+6) = 0\\\Rightarrow w =7, -6[/tex]
Dimensions can not be negative, so width, w = 7 ft
Height = (w-1) = 7-1 = 6 ft
So, the dimensions are 12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft.
In the flowering plant, white flowers (B) are dominant over red flowers (b), and short plants (E) are dominant over tall flower (e). An F2 generation was created by crossing two F1 individuals (each BbEe). The data below are the counted number of flowers from each phenotype in the F2 generation.
White short= 206
Red, short= 83
White, tall= 85
Red, tall= 30
Required:
a. What is your null hypothesis?
b. What is your expected phenotypic ratio based on Mendelian inheritance?
Question Completion
(a)What is your null hypothesis?
(b)What is your expected phenotypic ratio based on Mendelian inheritance?
(c)Calculate the expected number of flowers you should have gotten based on the Mendelian inheritance. Then calculate a chi-square value, degrees of freedom, and a p-value.
Chi-square statistic: _____Degrees of freedom (# phenotypes -1): P-value:(d)Interpret your results. Do you reject it or fail to reject your null hypothesis (please restate the null)?
Answer:
(a)[tex]H_0:$The given data fit the predicted phenotype[/tex]
(b)9:3:3:1
(c)
Chi-square statistic: 3.8914Degrees of freedom (# phenotypes -1) =3P-value: 0.2734(d)We fail to reject the null hypothesis.
Step-by-step explanation:
In the flowering plant, white flowers (B) are dominant over red flowers (b), and short plants (E) are dominant over tall flowers (e). An F2 generation was created by crossing two F1 individuals (each BbEe).
(a)The null hypothesis is:
[tex]H_0:$The given data fit the predicted phenotype[/tex]
(b)The gametes are BE, Be, bE and be.
The offsprings are presented in the table below:
[tex]\left|\begin{array}{c|cccc}&BE&Be&bE&be\\--&--&--&--&--\\BE&BE&BE&BE&BE\\Be&BE&Be&BE&Be\\bE&BE&BE&bE&bE\\be&BE&Be&bE&be\end{array}\right|[/tex]
The expected phenotypic ratio based on Mendelian inheritance
BE:Be:bE:be=9:3:3:1
(c)
[tex]\left|\begin{array}{c|c|c|c|c|c}$Phenotype&Observed&$Expected&O-E&(O-E)^2&\dfrac{(O-E)^2}{E} \\-----&--&--&--&--&--\\$White short(BE)&206&\frac{9}{16}*404 \approx 227 &-21&441&1.9427\\$Red, short(bE)&83&\frac{3}{16}*404 \approx 78 &5&25&0.3205\\$White, tall(Be)&85&\frac{3}{16}*404 \approx 78 &7&49&0.6282\\$Red, tall(be)&30&\frac{1}{16}*404 \approx 25 &5&25&1\\-----&--&--&--&--&--\\$Total&404&--&--&--&3.8914\end{array}\right|[/tex]
Therefore:
Chi-square statistic: 3.8914Degrees of freedom (# phenotypes -1): 4-1 =3P-value: 0.2734(d) Our null hypothesis is:
[tex]H_0:$The given data fit the predicted phenotype[/tex]
Since p>0.05, the given data fit the predicted phenotypic ratio.
We, therefore, fail to reject the null hypothesis.
The difference in the observed and expected are sosmall that they can be attributed to random chance.
The composite figure shown is made up of a cylinder and a___a0.
Answer: Cone
Step-by-step explanation:
Looking at the shape, the problem already listed cylinder. That is the bottom figure. The top figure is a cone.
Answer: cone
Step-by-step explanation:
The bottom figure is a cylinder. A cylinder is basically a rectangle wrapped around two circles.
The top figure is a cone. A cone’s net looks like a triangle with a curved base wrapped around a circle. If you don’t believe the top figure is a cone, think about what ice cream cones look like. The top figure is a cone.
Pls hit the thx button and mark me brainliest if this helped :)
Point D' is the image of D(-2, 1) under a reflection across the x-axis.
Answer:
-2, -1
Step-by-step explanation:
the x same cause if you reflect across the x-axis so you move on the y-axis. and reflect means the same distance from the point you reflect (that it was 1 cause it was 1 point above the x-axis) just negative so -1 now. if the original point was -2,-1 so the answer was -2,1.
a television set was sold during a clearance sale for dollar 299.00the television was sold at a discount of 70 percent, what was the list price?
Answer:
$996.67
Step-by-step explanation:
The discounted price is ...
(list price)(100% -70%) = $299.00
list price = $299.00/0.30 . . . . . divide by 0.30
list price = $996.67
How many cups of pineapple juice are needed to make 6 gallons of punch
Answer:
17
Step-by-step explanation:
A family uses 12,986.64 Swiss francs per year to pay a mortgage that requires US dollars. Approximately how much, in US dollars, does the family spend per month on the mortgage?
1 US dollar = 0.9019 Swiss francs
1 Swiss franc = 1.11 US dollar
A.)$975
B.)$1,080
C.)$1,200
D.)$1,440
Answer:
C
Step-by-step explanation:
Per year: 12,986.64 * 1.11 = 14,415.1704 US dollars
Per month: 14,415.1704/12 = 1,201.2642 US dollars
Answer: c 1,200
explanation: 1,200 ÷ 12,986.64 = 0.09240265Daley went to the grocery store to buy berries. Blueberries cost $1.50 a pound and strawberries cost $2.25 a pound. Daley spent $10.50 on fruit. The equation he wrote to represent the scenario is 1.5b + 2.25s = 10.5. His solution is: 1. Subtract 2.25s: 1.5b = 10.5 − 2.25s 2. Divide by 1.5: 1.5b 1.5 = 10.5 − 2.25s 1.5 3. Distribute 1.5: b = 7 − 1.5s Daley wrote an equivalent equation to determine how many pounds of blueberries he could buy. Analyze Daley’s work. Did he make an error? Yes. In step 1, he had to subtract 1.5b from both sides. Yes. In step 2, he had to multiply 1.5 to both sides. Yes. In step 3, he can only multiply the 1.5 and 12.5 together. No. He correctly solved for b.
Answer: 1.5(b)+ 2.25(s) = 10.05
Step-by-step explanation:
Answer:
B & S
Step-by-step explanation:
Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.
Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) y(x) = (explicit solution)
h = 0.1
xn yn Actual Value Absolute Error % Rel. Error
1.00 1.0000 1.0000 0.0000 0.00
1.10 1.2337 1.20 1.5527 1.30 1.9937
1.40 2.6117 1.50 3.4903
h = 0.05
xn yn Actual Value Absolute Error % Rel. Error
1.00 1.0000 1.0000 0.0000 0.00
1.05 1.1000 1.1079 0.0079 0.71
1.10 1.2155 1.2337 0.0182 1.48
1.15 1.3492 1.3806 0.0314 2.27
1.20 1.5044 1.5527 0.0483 3.11
1.25 1.6849 1.7551 0.0702 4.00
1.30 1.8955 1.9937 0.0982 4.93
1.35 2.1419 2.2762 0.1343 5.90
1.40 2.4311 2.6117 0.1806 6.92
1.45 2.7715 3.0117 0.2402 7.98
Answer:
see below for the tables
Step-by-step explanation:
The differential equation is separable, so the solution is ...
[tex]\displaystyle\dfrac{dy}{dx}=2xy\\\\\int{\dfrac{dy}{y}}=\int{2x}\,dx\\\\\ln{y}=x^2+C\\\\\text{Considering the initial condition, $C=-1$}\\\\\boxed{y=e^{x^2-1}}[/tex]
__
The values for yn are y+y'·h = y+2xyh. We take the "absolute error" to be the (signed) difference between the calculated yn and the actual value y(x).
Does anyone know the answer?
Answer:
5.44
Step-by-step explanation:
From Trigonometry Identity,
Sin65= CB/AB
CB = AB Sin65
= 6 × Sin65
= 5.4378
= 5.44{ to the nearest hundredth}
A new car is purchased for 25000 dollars.The value of the car depreciates at 8.25% per year.What will the value of the car be,to the nearest cent,after 15 years?
Answer:
da,
Step-by-step explanation:
line a passes through (0,3) & (-4,8) line b passes through (0,5) & (5,9) lines a & b are?
Answer:
line a )y=-5/4x+3
line b) y=4/5+5
If the following inequality is divided by −2, what is the resulting inequality? −2x≤−20
Step-by-step explanation:
When dividing by a negative number, you "flip" the inequalities sign so you would divide -20 by -2 which would leave you with 10. X is left where it is and you flip the inequalities sign to a ≥ sign.
final answer =
x ≥ 10
Natasha's sculpture was 5 3/16 inches tall. Mayas was 4 times as tall.How much shorter was Natasha's sculpture than Mayas
Answer:
Natasha's sculpture is 249/16 or 15.5625 or 15 9/16 inches shorter than Mayas sculpture
Step-by-step explanation:
The height of Natasha sculpture is 5 3/16 inches tall. Let us convert the height to an improper fraction.
5 3/16 = 83/16 inches tall. Therefore,
Natasha's sculpture is 83/16 inches tall.
According to the question Mayas own sculpture was 4 times as tall as Natasha's own sculpture. Mathematically, Mayas sculpture height can be expressed as follows
Mayas sculpture height = 4(83/16)
Mayas sculpture height = 4 × 83/16
Mayas sculpture height = 332/16
Mayas sculpture height = 20.75 inches or 83/4 inches
To know how much shorter was Natasha's sculpture we subtract Natasha sculpture height from Mayas sculpture height.
Therefore,
83/4 - 83/16 = (332 - 83) /16 = 249/16 or 15.5625 or 15 9/16
Natasha's sculpture is 249/16 or 15.5625 or 15 9/16 inches shorter than Mayas sculpture
Find 3 points that solve the equation -x + 2y= 2
Answer:
(0,1)
(-2,0)
(2,2)
Step-by-step explanation:
Solve the two-step equation. -9x + 0.4 = 4 Which operation must be performed to move all the constants to the right side of the equation? Then, which operation must be performed to isolate the variable? The solution to the equation is x = .
Answer:
x = -0.4
Step-by-step explanation:
We have the equation:
-9x + 0.4 = 4
First, the operation to move all the constants to the right side is subtraction since we would have to subtract 0.4 from each side, let's see this:
[tex]-9x+0.4=4\\-9x+0.4-0.4=4-0.4\\-9x=3.6[/tex]
Now, we have all the constants on the right side of the equation.
Now, the operation we need to perform to isolate the variable is division (since the x has a -9 that is being multiplied by x) we need to do the opposite operation:
[tex]-9x=3.6\\\frac{-9x}{-9} =\frac{3.6}{-9} \\x=-0.4[/tex]
Thus, the answer to this equation is x= -0.4
Answer:
1.) Which operation must be performed to move all the constants to the right side of the equation?
✔ Subtract 0.4 (C)
2.) Then, which operation must be performed to isolate the variable?
✔ Divide by -9 on both sides. (D)
3.) The solution to the equation is x =
✔ -0.4 (B)
Step-by-step explanation:
I hope this helps!! Have a wonderful day!! :))
Which product is negative? (Negative StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (one-fourth) (StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (Negative one-fourth) (StartFraction 3 over 8 EndFraction) (StartFraction 5 over 7 EndFraction) (one-fourth) (Negative StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (negative one-fourth)
Answer:
[tex](D)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)[/tex]
Step-by-step explanation:
The given options are:
[tex](A)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(\dfrac14\right)\\(B)\left(\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)\\(C)\left(\dfrac38\right)\left(\dfrac57\right)\left(\dfrac14\right)\\(D)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)[/tex]
The key to determining which product is negative is to understand the rule of sign multiplication.
Now:
The product of even negative terms is positiveThe product of odd negative terms is negative.The product of positive will always be positive.In Options A and B, the number of negative signs is even, therefore our result is positive.
In option C, all the terms are positive, therefore our result will be positive.
In Option D, the number of negative signs is odd, therefore our result is negative.
Answer:
your answer is D
:)
Find the area of the figure. (Use “sq units” as the units of measure) Hints: Break it down into the triangle and 2 rectangles. Pay attention to the measurements.
Answer:
Area of the figure is 60.75 m²
Step-by-step explanation:
If we divide the given figure in three parts,
Area of the figure = Area of rectangle (1) + Area of rectangle (2) + Area of triangle (3)
Area of rectangle (1) = (Length × width)
= 3 × 4.5
= 13.5 m²
Area of rectangle (2) = (12 × 3)
= 36 m²
Area of triangle (3) = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(7.5)(3)[/tex]
= 11.25 m²
Area of the complete figure = 13.5 + 36 + 11.25
= 60.75 m²
Therefore, area of the figure is 60.75 m²
What is the value of x?
Answer:
x=-14
Step-by-step explanation:
The 2 angles are opposite of each other. This means that they are vertical angles, are they are congruent.
Since they are congruent, we can set them equal to each and solve for x.
9x+184=7x+156
To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
First, subtract 7x from both sides.
9x-7x+184=7x-7x+156
9x-7x+184=156
2x+184=156
Next, subtract 184 from both sides.
2x+184-184=156-184
2x=156-184
2x=-28
Finally, divide both sides by 2.
2x/2= -28/2
x=-28/2
x= -14
The value of X is -14.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
( 3/4 ÷ 3/100 −23 1/2 )÷1 1/2 · 2/3 +1 1/6
All of the (/) are fractions. Sorry if it's unclear.
Answer:
Simplify: = −7333 4400 (Decimal: -1.666591)
Answer: −7333/ 4400
Step-by-step explanation:
Steps below
1: 343100−2312112(2)3+116
2: 14100−2312112(2)3+116
3: 1400−2312112(2)3+116
4: −46199400112(2)3+116
Answers:
Simplify: = −7333 4400 (Decimal: -1.666591)
Answer: −7333/ 4400
Hope this helps.
Answer:
The answer is 11/6
Solve the formula for c
m=h/c-w
Answer:
c = h/(m+w)
Step-by-step explanation:
m=(h/c)-w
Add w to each side
m+w=h/c-w+w
m+w = h/c
Multiply each side by c
c(m+w) = h/c*c
c(m+w) = h
Divide each side by (m+w)
c(m+w)/(m+w) = h/(m+w)
c = h/(m+w)
help, surface area. will mark brainliest!
Answer:
3024
Step-by-step explanation:
Find the area of the isosceles triangles, and add then with the three rectangles to get surface area.
14*24/2 * 2 = 336, and you have 25*42 * 2 = 2100, and finally you have 14*42 = 588. so the sum should be 3024
The rectangle has a length of 4x+3 and a width of 3x. Show your work.
A. Find the perimeter.
B. Find the area.
C. Find the perimeter and area if x = 8.
Answer:
A. P = 14x+6
B. A = 12x^2 +9x
C. P = 118; A = 840
Step-by-step explanation:
A. The perimeter is twice the sum of length and width:
P = 2(L +W) = 2((4x+3) +(3x)) = 2(7x +3)
P = 14x +6 . . . . the perimeter of the rectangle
__
B. The area is the product of length and width:
A = LW = (4x +3)(3x)
A = 12x^2 +9x . . . . . the area of the rectangle
__
C. When x = 8, these values are ...
P = 14·8 +6 = 118 . . . . . perimeter in units
A = 12·8^2 +9·8 = 768 +72 = 840 . . . . . area in square units
Answer:
a) [tex] P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6[/tex]
b) [tex] A= 12x^2 +9x[/tex]
c) [tex] P = 14*8 +6 = 112+6 = 118[/tex]
[tex] A= 12(8)^2 +9*8 = 840[/tex]
Step-by-step explanation:
We know that the length is 4x+3 and the width is of 3x
Part a
For this case the perimeter is given by:
[tex] P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6[/tex]
Part b
The area is given by:
[tex] A= (4x+3) (3x)[/tex]
And after multiply we got:
[tex] A= 12x^2 +9x[/tex]
Part c
For this case replacing the value of x =8 we got:
[tex] P = 14*8 +6 = 112+6 = 118[/tex]
[tex] A= 12(8)^2 +9*8 = 840[/tex]
Adam works for an agency
341 is 55% of what number? Round your answer to the nearest hundredth
Your answer will be 620!
Answer:
the number is 620.
Step-by-step explanation:
in other words the question is 55% of what number is 341?
let the number be Y.
[tex]\frac{55}{100}*Y=341[/tex]
[tex]\frac{55Y}{100}=341[/tex]
[tex]55Y=341*100[/tex]
[tex]55Y=34100[/tex]
[tex]Y=\frac{34100}{55}[/tex]
Y=620
According to R.L. Polk & Co., the average age of cars and light trucks in the U.S. is 10.8 years. Assume that the standard deviation for this population is 3.7 years. A sample of 35 randomly selected vehicles was selected. What is the probability that the sample mean will be greater than 10 years?
Answer:
10.03% probability that the sample mean will be greater than 10 years
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 10.8, \sigma = 3.7, n = 35, s = \frac{3.7}{\sqrt{35}} = 0.6254[/tex]
What is the probability that the sample mean will be greater than 10 years?
This is 1 subtracted by the pvalue of Z when X = 10. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{10 - 10.8}{0.6254}[/tex]
[tex]Z = -1.28[/tex]
[tex]Z = -1.28[/tex] has a pvalue of 0.1003
10.03% probability that the sample mean will be greater than 10 years
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Tangents that meet at a point are equal in length so JL and LM are equal
Let's form an equation:
3x + 10 = 7x - 6
+6 to both sides
3x + 16 = 7x
-3x from both sides
16 = 4x
/4 on both sides
x = 4
Now, we can sub this value into the equation:
7(4) - 6 = 22
Thus, your answer is option B. 22
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
2ND OPTION
Step-by-step explanation:
in a circle , tangents drawn from an external point to the circle are equal.
ie JL = LM
3x+10 = 7x-6
10 + 6 = 7x- 3x
16 = 4x
x = 16/4
x=4
therefore LM = 7x -6 = 7*4 - 6
LM = 28 - 6 =22
therefore LM =22
HOPE IT HELPS. PLEASE MARK ME AS THE BRAINLIEST....
Find the equation of the line.
(6,4) (-4,-5)
Answer:
y = (9 x)/10 - 7/5
Step-by-step explanation:
y-y/x-x
60 POINTS Explain the process and solve a logarithmic equation. log x + log 8 – 2log 4 = 7.
Answer:
[tex]x = 20000000[/tex]
Step-by-step explanation:
Recall the power property of logarithms which states:
[tex]log(a^n)=n\,\,log(a)[/tex]
to re-write [tex]2\,log(4)=log(4^2)=log(16)[/tex]
and then use the product and quotient rules of logarithms:
[tex]log (A*B)=log(A)+log(B)[/tex]
and
[tex]log (\frac{A}{B} )=log(A)-log(B)[/tex]
to rewrite the combination of logarithms on the left of the equal sign as a single logarithm:
[tex]log(x)+log(8)-2\,\,log(4)=7\\log(x)+log(8)-log(16)=7\\log(\frac{8\,x}{16}) =7\\log(\frac{x}{2}) =7[/tex]
and now re-write this equation in exponent form to get rid of the logarithm:
[tex]10^7=\frac{x}{2} \\2\,\,\,10^7 = x\\x = 20000000[/tex]
Conduct the following test at the alpha = 0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume that the samples were obtained independently using simple random sampling.
Test whether p1 not equals p2. Sample data are x1 = 28, n1 = 254, x2 = 38, and n2 = 301.
Answer:
a) H0: p1 - p2 = 0
H1: p1 - p2 ≠ 0
b) z=-0.58
c) p-value = 0.562
Step-by-step explanation:
We need to determine whether p1 is not equals p2, so the null and alternative hypothesis are:
H0: p1 - p2 = 0
H1: p1 - p2 ≠ 0
Where p1 and p2 are the proportions of the population. Additionally, the proportions of the sample p1' and p2' are calculated as:
[tex]p1'=\frac{x1}{n1}=\frac{28}{254}=0.1102\\p2'=\frac{x2}{n2}=\frac{38}{301}=0.1262[/tex]
Then, the test statistic is calculated using the following equation:
[tex]z=\frac{(p1'-p2')-(p1-p2)}{\sqrt{p'(1-p')(\frac{1}{n1}+\frac{1}{n2})} }[/tex]
Where p' is calculated as:
[tex]p'=\frac{x1+x2}{n1+n2}=\frac{28+38}{254+301}=0.1189[/tex]
So, replacing the values, we get that the test statistic is:
[tex]z=\frac{(0.1102-0.1262)-(0)}{\sqrt{0.1189(1-0.1189)(\frac{1}{254}+\frac{1}{301})}}=-0.58[/tex]
Finally, using the standard normal table, the p-value is equal to:
[tex]p-value=2*P(z<-0.58)=2*0.281=0.562[/tex]
The p-value is greater that the value of alpha 0.1, so we can't reject the null hypothesis and there is evidence to said that p1 and p2 are equals.
Suppose we want to choose a value of x at least 5 units away from 14.A) Think about some values of x that meet this constraint.B) Write an inequality that represents all values of x that meet this constraint. Hint. no answer givenC) On the number line below, represent all values of x that meet this constraint. Clear All Draw: Line segments and raysClosed dotOpen dot
Answer:
(a) [9, 19]
(b) [tex]9 \leq x \leq 19[/tex]
(c)See attachment
Step-by-step explanation:
We want to choose a value of x at least 5 units away from 14.
(a)Now, 14-5=9 and 14+5=19
The possible values of x ranges is in the closed interval [9,19]
(b) Since x is at least 5 units away from 14, we have:
[tex]|14-x|\leq5[/tex]
Solving the absolute inequality
[tex]-5 \leq 14-x \leq 5\\$In $ -5 \leq 14-x\\ x \leq 14+5\\x \leq 19\\\\$In $ 14-x \leq 5\\ 14-5 \leq x\\9 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\9 \leq x \leq 19[/tex]
(c)To draw the number line, we use a closed dot since we have a less than or equal to sign.
Inequalities are used to represent unequal expressions.
The inequality that represents the scenario is [tex]\mathbf{|x-14| \ge 5}[/tex]Some possible values of x are: 5 and 20Represent the value with x.
A value that is at least 5 from 14 can take any of the following forms:
[tex]\mathbf{14 -x \ge 5}[/tex]
[tex]\mathbf{x-14 \ge 5}[/tex]
The inequalities can be combined as:
[tex]\mathbf{|x-14| \ge 5}[/tex]
The values of x are solved as follows:
[tex]\mathbf{14 -x \ge 5}[/tex]
[tex]\mathbf{14 - 5 \ge x}[/tex]
[tex]\mathbf{9\ge x}[/tex]
Rewrite as:
[tex]\mathbf{x \le 9}[/tex]
Similarly, we have:
[tex]\mathbf{x-14 \ge 5}[/tex]
[tex]\mathbf{x \ge 14 + 5}[/tex]
[tex]\mathbf{x \ge 19}[/tex]
So, we have:
[tex]\mathbf{x \le 9}[/tex] or [tex]\mathbf{x \ge 19}[/tex]
This can be combined as:
[tex]\mathbf{9 \ge x \ u\ x \ge 19}[/tex]
Some possible values of x are: 5 and 20
Read more about inequalities at:
https://brainly.com/question/1930605