The amount Cindy should increase for each dimension of the scaled model will be 12 meters.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
Given that:-
The scaled model of the container has dimensions of 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model.The scale model will be solved as follows:-
Present volume = 2 x 4 x 6 = 48 cubic meters
Let the lengths be increased by x meters now the new volume will be:-
( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84
( x² + 6x + 8 ) ( 6 + x ) = 48 x 84
( x³ + 44x + 12x² - 3984 ) = 0
By solving the cubic equation we will get the value of x = 12 meters.
Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.
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For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2)
70. f(x) = 8x2 − 7x + 3
Answer:
See below. I assume that (x) = 8x2 - 7x + 3 is really (x) = 8x^2 - 7x + 3
Step-by-step explanation:
Substitute the value of x given in f(x) into the equation f(x) = 8x^2 - 7x + 3
For example, f(0) would be f(0) = 8(0)^2 - 7(0) + 3. f(0) = 3
f(-2) would be f(-2) = 8(-2)^2 - 7(-2) + 3.
= 8*4 + 14 +3
= 32 + 17 therefore f(-2) = 49
x f(x)
-2 49
-1 18
0 3
1 4
2 21
Find the perimeter
a = x +3
b = 2x - 1
Answer:
Step-by-step explanation:Rectangles have 4 sides--2 = lengths and 2 = widths, so perimeter = 2l + 2 w = 2(l + w).
l + w = (2x - 1) + (x + 3) = 3x + 2. Then double with distributive property P = 2(3x + 2)
P = 6x + 4
You could also do distributive property twice: 2(2x - 1) + 2(x + 3) = 4x - 2 + 2x + 6 = 6x + 4.
Solve for u.
u^2+9u+14=0
If the measure of angle 2 is 92 degrees and the measure of angle 4 is (one-half x) degrees, what is the value of x? 2 lines intersect to form 4 angles. from top left, clockwise, the angles are 1, 4, 3, 2. 46 88 92 184
The value of x is 184.
What is the value of x?
Given Information
The measure of angle 2 = 92°
The measure of angle 4 = (x/2)°
From the figure, it can be seen that angle 2 and 4 make vertically opposite angles.
Vertically Opposite Angles
The pair of angles that are formed by two intersecting lines and are opposite to each other are defined as vertically opposite angles. The values of vertically opposite angles are always equal.
Here, in this case, ∠1 and ∠3 make a pair of vertically opposite angles. ∠2 and ∠4 form another pair of vertically opposite angles. Hence,
∠4 = ∠2
(x/2) = 92
x = 92 × 2
x = 184
Thus, the value of x is 184.
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Answer:
184
Step-by-step explanation:
edge
Factor the polynomial: x2+7x+12 A (x + 3)(x + 4) B (x + 2)(x + 6) C (x + 1)(x + 12) D (x + 7)(x + 12)
Answer:
a: (x + 3)(x + 4)
Step-by-step explanation:
assuming x^2 + 7x + 12 is the equation you are factoring
you would first multiply a * c
a is 1
b is 7
c is 12
1 * 12 = 12
then you take b and find what adds up to b but multiplies to ac
what adds up to 7 but multiplies to 12
3 and 4
so
you split the equation up like this
x^2 + 3x + 4x + 12
then you factor
x(x + 3) + 4(x + 3)
because x + 3 and x + 3 are the same we can do this
(x + 4)(x + 3)
that is your equation
so a is your answer
it doesnt matter if you have the (x + 3) or (x + 4) in the front
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]
-------------------------------------------------------------------------------------------------------------
In order to factor the polynomial we need to first split the middle term so it add up to 7 but multiplies to 12. We know that 3 and 4 can do that. We would the factor by grouping which would give us our final answer.
[tex]x^2 + 7x + 12[/tex]
[tex]x^2 + 4x + 3x + 12[/tex]
[tex]x(x + 4) + 3(x + 4)[/tex]
[tex](x + 3)(x + 4)[/tex]
Answer: [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]
ista father has an age that is 2 years greater than four times her age.The sum of their ages is 57 yeasrs
Answer:
Ista is 11 years old. Her father is 46 years old.
Step-by-step explanation:
Let ista's age be x.
Fathers age=4x+2.
Fathers age + Ista's age = 57.
4x+2+x=57.
Combine like terms:
5x+2 -2 =57 -2
5x=55
x=11
Fathers age: 4(11)+2
= 46
If ista father has an age that is 2 years greater than four times her age. The sum of their ages is 57 years. Then ista age is 11 and her father age is 46.
What is Equation?Two or more expressions with an equal sign is called as equation.
Given that,
ista father has an age that is 2 years greater than four times her age.The sum of their ages is 57 yeasrs
Let the age of ista be x.
ista father has an age that is 2 years greater than four times her age.
it means father age = 2+4x
The sum of ista age and her father age is 57.
So x+(2+4x)=57
Add the common terms
5x+2=57
Subtract 2 from both sides
5x=55
Divide both sides by 5
x=11
Hence ista age is 11 and her father age is 46.
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What is the length of the hypotenuse for the triangle shown? Write your answer in simplest radical form. Show all of
your work for full marks. (Hint: Use Pythagorean Theorem).
Answer:
Step-by-step explanation:
do a squared plus b squared = c squared like
2 and 5 thingy squared by 2 + 6 squared = c squared
unsquare c and you get your answer
Algebra 1 A Adaptive CR (JL22) 1/Tools Of The Trade
2. Simplify and write in exponential form. (4³)(3) = ?
O
O (4³) (¹)
521
The simplified expression of [tex](4^3)(\frac{4^4^0x^4}{3^2x^2y^2})[/tex] is [tex]\frac{4^7x^2}{3^2y^2}[/tex]
How to simplify the expression?The expression is given as:
[tex](4^3)(\frac{4^4^0x^4}{3^2x^2y^2})[/tex]
Expressions raise to power 0 is 1.
So, we have:
[tex](4^3)(\frac{4^4x^4}{3^2x^2y^2})[/tex]
Apply the law of indices to expression with common base
[tex](\frac{4^{4+3}x^{4-2}}{3^2y^2})[/tex]
Evaluate the sum and difference
[tex](\frac{4^7x^2}{3^2y^2})[/tex]
Remove the bracket
[tex]\frac{4^7x^2}{3^2y^2}[/tex]
Hence, the simplified expression of [tex](4^3)(\frac{4^4^0x^4}{3^2x^2y^2})[/tex] is [tex]\frac{4^7x^2}{3^2y^2}[/tex]
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John is a quarterback. This year, he completed 350 passes, which is 70%, percent of all the passes he's attempted this year.
How many passes has John attempted this year?
If a > b > c > d, then which is larger, a+c or b+d ? Can we tell from a > b > c > d which of a+d and b+c is larger?
Answer:
1. a+c is larger than b+d
2. No way to tell whether a+d or b+c is larger.
Step-by-step explanation:
1. Which is larger, a+c or b+d?
Let a, b, c, and d be any numbers such that [tex]a > b > c > d[/tex].
Specifically, note that [tex]a > b[/tex], and subtracting b from both sides of the inequality, observe that [tex]a-b > 0[/tex].
Similarly, [tex]c > d[/tex], and subtracting d from both sides of the inequality, observe that [tex]c-d > 0[/tex].
From this, add "a-b" (a positive number, as proven above) to both sides of the inequality.
[tex](a-b)+(c-d) > (a-b)+0[/tex]
Addition by zero (the additive identity) doesn't change anything, so the right side remains "a-b"...
[tex](a-b)+(c-d) > a-b[/tex]
... and "a-b" is positive...
[tex](a-b)+(c-d) > a-b > 0[/tex]
... so, by the transitive property of inequality...
[tex](a-b)+(c-d) > 0[/tex]
Recall that subtraction is addition by a negative number...
[tex]a+(-b)+c+(-d) > 0[/tex]
...and that addition is associative and commutative, so things can be added in any order, so the middle two terms on the left side can be rearranged...
[tex]a+c+(-b)+(-d) > 0[/tex]
Adding b + d to both sides of the inequality
[tex](a+c+(-b)+(-d))+(b+d) > 0+(b+d)[/tex]
... and simplifying
[tex]a+c > b+d[/tex]
So, a+c is larger than b+d.
2. Which is larger, a+d or b+c?
Consider the following two examples:
Example 1
Suppose a=10; b=3; c=2; d=1.
Note that [tex]a > b > c > d[/tex] ([tex]10 > 3 > 2 > 1[/tex]) and, also observe that [tex]a+d=(10)+(1)=11[/tex], and [tex]b+c=(3)+(2)=5[/tex], so a+d is larger than b+c.
Example 2
However, suppose a=10; b=9; c=8; d=1.
Note that [tex]a > b > c > d[/tex] ([tex]10 > 9 > 8 > 1[/tex]) but that [tex]a+d=(10)+(1)=11[/tex], and [tex]b+c=(9)+(8)=17[/tex], so a+d is smaller than b+c.
So, in one example, a+d is bigger, and in the other, a+d is smaller. Therefore, there is no way to tell which of a+d or b+c is larger from only the given information.
do any questions that you can from any page!!!! I will still give you the points! Show your work, please!!!! literally do whatever you can!!!!!
Answer:
I think that the awnser to 59 is 24x⁴-15x²+27x
x-11<36 need help on this equation
Answer:
x<47
Step-by-step explanation:
Take -11 to the side which 36 is. Once it crosses it stops being negative and becomes positive so the equation becomes x<36+11 which is x<47
The value represents the number of times the interest is compounded in a year.
The compound periods and Interest rates for compound interest have been explained below.
How to define compound interest terms?
1) Compound Periods (n); If we want to calculate the compound interest, the number of compounding periods makes a significant difference due to the fact that the higher the number of compounding periods, the greater the amount of compound interest.
2) Interest rate per compounding periods (I); This affects the interest rate compounded annually due to the fact that the interest rate will be compounded once a year.
Complete question is;
In your own words and using visuals, explain the following. Regarding compound interest, how does the number of times interest is compounded per year affect the:
a) number of compounding periods (n)
b) interest rate per compounding period (i)
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A retail shop accepts only cash or checks. Suppose that 60% of its customers carry cash, 59% carry checks, and 77% carry cash or checks (or both). What is the probability that a randomly chosen customer at the shop is carrying both cash and checks?
[tex]p(c) = 0.6 \\ p(ch) = 0.59 \\ p(any)= 0.77[/tex]
[tex]p(both) = p(c) + p(ch) - p(any) \\ p(both) = 0.6 + 0.59 - 0.77 \\ p(both) = 0.42[/tex]
helllppppppppppp please
Answer:
7x-13y=-117
Step-by-step explanation:
I don't know how this question wants me to solve it, but I just used the slope intercept form. So first, start off with y = mx+b. Plug in the slope for m, so 7/13. Then plug in your points for x,y which is 0,9. You'll get 9 = b. So then you have y = 7/13x+9. So now you need to change into standard form. So, multiply by the denominator (13) and you'll get 13y = 7x+117. Then move the variable over and you'll get 13y - 7x = 117. But it doesn't fit any, so then just multiply by -1 and you'll get -13y + 7x = -117.
A flower garden measures 14cm by 20cm. There is a path 2m wide all round it. Find the area of the path.
Answer:
152 m²
Step-by-step explanation:
Area of flower garden
Assuming the flower garden is rectangular and its dimensions are measured in meters:
width of garden = 14 mlength of garden = 20 m[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies \textsf{Area of flower garden} & = \sf 14 \times 20\\& = \sf 280\:\:m^2 \end{aligned}[/tex]
Total area of path and garden
If there is a 2 m wide path all around the garden, the dimensions of the total area will be the dimensions of the garden extended by 4 m:
width = 14 m + 2 m + 2 m = 18 mlength = 20 m + 2 m + 2 m = 24 m[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies \textsf{Total area} & = \sf 18 \times 24\\& = \sf 432\:\:m^2 \end{aligned}[/tex]
Area of path
To calculate the area of the path, subtract the area of the garden from the total area:
[tex]\begin{aligned}\implies \textsf{Area of path} & = \sf Total\:area-Area\:of\:garden\\& = \sf 432-280\\& = \sf 152\:\:m^2 \end{aligned}[/tex]
write the equation of a circle with a center at (1,-9) and a radius of 12
The equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
How to determine the circle equation?The given parameters are:
Center, (a,b) = (1, -9)
Radius, r = 12
The circle equation is calculated as:
(x - a)^2 + (y- b)^2 = r^2
This gives
(x - 1)^2 +(y + 9)^2 = 12^2
Evaluate the exponent
(x - 1)^2 +(y + 9)^2 = 144
Hence, the equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
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According to the 2010 Census, 13% of all housing units in the United States were vacant. A Vigo County supervisor wonders if her county is different from this. She randomly selects 550 housing units in her county and finds that 130 of the housing units are vacant. Conduct an appropriate hypothesis test for the supervisor and state your conclusion.
The conclusion is that there is sufficient evidence to support the claim that the percentage of vacant housing units in their district differs from the percentage of vacant housing units in the country.
Given that the total number of a housing units in her country is 550 and the number of vacant housing units in her country is 130.
The Null hypothesis is p₀=13%=0.13, n=550 and x=130
Significance level α=0.05
Claims given: percentage other than 13%
The claim is anyone of the null hypothesis or the alternative hypothesis. The null hypothesis shows that the proportion of the population is equal to the value stated in the claim. If the null hypothesis is a claim, then the alternative hypothesis states the opposite of the null hypothesis.
H₀:p=13%=0.13
Hₐ:p/0.13
I'm interested in testing population proportion claims, so I'll use z-text with proportions.
Conditions: Random sample, 10% condition, pass / fail condition
Sample: I'm happy because the housing units were randomly selected. 10% Condition: We are happy because the sample of 550 homes in your county is less than 10% of the population.
Pass/ fail condition: Satisfied because both np₀ and n(1-p₀) are both at least 10.
np₀=550(0.13)=71.5≥10
n(1-p₀)=550(1-0.13)=478.5≥10
Therefore, we conclude that all the conditions are met.
The sample percentage is the number of successes divided by the sample size.
[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{130}{550}\\ &\approx 0.2364\end[/tex]
Determines the value of the test statistic:
[tex]\begin{aligned}z&=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \\ &=\frac{0.2364-0.13}{\sqrt{\frac{0.13(1-0.13)}{550}}}\\ &=\frac{0.1064}{0.0143}\\&\approx 7.41 \end[/tex]
The P-value is the probability of getting a test statistic value or a more extreme value if the null hypothesis is true. Use the normal probability table in the appendix to determine the P-value.
P=P(Z<−7.41 or Z>7.41)
P=2P(Z>7.41)
P=2(0)
P=0
If the P-value is less than the significance level α, the null hypothesis is rejected.
P<0.05⇒ Reject H₀
Therefore, there is ample evidence to support the claim that the proportion of vacant homes in the area is different from the proportion of vacant homes in the country.
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mark the congruent parts of the triangles and complete the proof
1) given
2) definition of an angle bisector
3) reflexive
4) [tex]\triangle ABD \cong \triangle CBD[/tex] (ASA)
5) [tex]\angle A \cong \angle C[/tex] (CPCTC)
The average velocity of 25 taxies is 40 km/hr and the velocity of 35 trucks is 30 km/ hr. find the combined average velocity of both types of vehicles.
Answer:
70 km/hr
Step-by-step explanation:
You just have to add both of the average velocity as you are finding the combined average velocity of both vehicles
The cost of attending an amusement park is $10 for children and $20 for adults. On a particular day, the attendance at the amusement park is 30,000 attendees, and the total money earned by the park is $500,000. Use the matrix equation to determine how many children attended the park that day. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 1 and row 2 is 10 and 20, is multiplied by matrix with 2 rows and 1 column, where row 1 is c and row 2 is a, equals a matrix with 2 rows and 1 column, where row 1 is 30,000 and row 2 is 500,000.
Based on the figures above, the numbers of children that attended the park that day is 10,000.
What is the matrix equation about?
Fist we have to use the determinant to solve for c and as such:
[tex]\frac{det.\frac{30000}{500000} \frac{1}{20} }{det. \frac{1}{10} \frac{1}{20} }[/tex]
=[tex]\frac{30000 x 20 - 500000 x 1}{1 x 20 - 1 x 10}[/tex]
= 100000/10
=10,000
Therefore, Based on the figures above, the numbers of children that attended the park that day is 10,000.
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While working at Jimmy John's last week, Hal noticed that he was running out of lettuce and became suspicious that the manufacturer was underfilling the lettuce bags. To see if the bags have the stated weight of 15 pounds, he randomly selected 13 bags and found a sample mean of 14.39 pounds with a sample standard deviation of 0.539 pounds. Is this
Yes, it is true that Jimmy John was underfilling the lettuce bags with sample mean of 14.39 pounds and sample standard deviation of 0.539.
Given sample mean =14.39 pound, sample standard deviation=0.539 and stated weight=15 pounds.
We know that mean is the number which comes after dividing sum of numbers divided by numbers. Standard deviation shows how much dispersed data is. Firstly we observe through mean and because it is less than 15, it means Jimmy John's had underfilled in atleast one bag otherwise if he had not underfilled the mean may come greater than or equal to 15 pounds.
Now come along standard deviation, we can observe that standard deviation is also low means the points are not in such a way that one point lies at 15 and other one is 25. It also shows underfilling of lettuce bags.
Hence it is true that Jimmy John had underfilled the lettuce bags.
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A certain drug decays at a rate of 10% per hour. If the initial dose is 700 mg, how much left in a person’s system after 5 hours?
50
---- ×700=350
100
700-350=350
Therefore 350 grams is left in a person's system after 5 hours
Which of the following ordered pairs is not a solution of the system of inequalities?
y> x² - 4x-5
y< -x - 5x+6
OA) (1,-5)
B) (-1,6)
OC) (1, -7)
OD) (1,7)
The ordered pair that is not a solution of the system of inequalities is the one in option D (1, 7).
Which of the following ordered pairs is not a solution of the system?
Here we have the system of inequalities:
y > x² - 4x-5
y < -x² - 5x+6
If at least one of the inequalities is false for the given ordered pairs, then the ordered pair is not a solution for the system.
Then we only need to evaluate all the ordered pairs on the given inequalities and see when we have one that is false.
If you look at the pair D (1, 7) and we evaluate that on the second inequality, we get:
7 < (1)² - 5*1 + 6
7 < -2
This is false, then (1, 7) is not a solution of the sytem.
The correct option is D.
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write the equation 12^-2 in simplest form
Answer:
0.00694444444444444444444444444444
Rounded to the nearest thousandths: 0.007
Step-by-step explanation:
Use calculator.
Hope this helps!
If not, I am sorry.
Add the following polynomials, then place the answer in the proper location on the grid
14x^2 - 8x + 3
-6x^2 + 7x - 11
The addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8
Polynomial(14x^2 - 8x + 3) + (-6x^2 + 7x - 11)
= 14x² - 8x + 3 - 6x² + 7x - 11
collect like terms= 14x² - 6x² - 8x + 7x + 3 - 11
= 8x² - x - 8
Therefore, the addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8
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Find the distance from the point (1, 0, -2) to the origin.
Answer:
.5
Step-by-step explanation:
Point = P (1, 0, -2)
Origin= 0 (0, 0, 0)
The distance formula in 3D = √(n2 - n1)² + (y2 - y1)² + (Z2 - Z1)²
= √(1 - 0)² + (0 - 0)² + (-2 - 0)²
= √1 + 4
= √5
How do you find the distance from a point to the origin?
As a special case of the distance formulation, think we need to recognize the distance of a point (x,y) to the beginning. in step with the gap formula, this is √(x−0)2+(y−0)2=√x2+y2. A point (x,y) is at a distance r from the starting place if and simplest if √x2+y2=r, or, if we square each aspect: x2+y2=r2.
Conclusion: The method to find the distance among the two factors is commonly given with the aid of d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the gap among any two factors on a coordinate aircraft or x-y plane.
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Find two consecutive even numbers
whose sum is 126.
Answer:
62 and 64
Step-by-step explanation:
Let x be the first number
Let y be the 2nd number
Given,
x + 2 = y (Consecutive even numbers)
x - y = -2 (rearranged) - Equation 1
x + y = 126 - Equation 2
Now we can solve for x and y to find the 2 numbers by using substitution method in solving simultaneous equations.
x = y-2 (rearranged equation 1)
Now we substitute equation 1 into equation 2.
y - 2 + y = 126
2y - 2 = 126
2y = 126 + 2
2y = 128
y = 128 / 2
= 64
Now we will substitute y into equation 1.
x - 64 = -2
x = -2 + 64
= 62
Therefore the 2 numbers are 62 and 64.
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Find two consecutive even numbers whose sum is 126.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
For now, let the first number be x.
Let the second number be x+2. (consecutive even numbers are right next to each other, like 2 and 4)
These two integers add up to 126. This gives us an equation that we can solve in terms of x.
[tex]\bf{x+x+2=126}[/tex] | arrange the like terms
[tex]\bf{2x+2=126}[/tex] | subtract 2
[tex]\bf{2x=124}[/tex] | 2 was subtracted from BOTH sides
[tex]\bf{x=62}[/tex]
[tex]\cline{1-2}[/tex]
Now, the second integer is [tex]\bf{x+2}[/tex].
[tex]\bf{So\;let's\;put\;the\;first\;number\;into\;the\;formula\;x+2}[/tex].
[tex]\bf{62+2}[/tex] | add (mental arithmetic)
[tex]\bf{64}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Number\;1=62}\\\\=Number\;2=64[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]
11. (08.03)
What are the factors of 3x² + 10x + 3? (4 points)
O (3x - 1)(x-3)
O (3x - 3)(x - 1)
O (3x + 1)(x+3)
O (3x+3)(x + 1)
Step-by-step explanation:
[tex] = 3 {x}^{2} + 10x + 3[/tex]
[tex] = 3 {x}^{2} + 9x + x + 3[/tex]
[tex] = 3x(x + 3) + 1.(x + 3)[/tex]
[tex] = (x + 3)(3x + 1)[/tex]
[tex] = (3x + 1)(x + 3)[/tex]
The answer is C.
In the picture, t || s, m∠1 = 10x + 2, and m∠2 = 12x – 22. Find the measure of angle 2.
Answer:
122
Step-by-step explanation:
Given information, line t is parallel to line s.
angle 1 and angle 2 are alternate angles and so their measure is equal to each other:
10x + 2 = 12x - 22 transfer like terms to the same side of the equation
2 + 22 = 12x - 10x
24 = 2x divide both sides by 2
12 = x to find the measure of angle 2 replace x with the value we found
12*12 - 22 = 122