Answer: Yes they form a proportion. The given equation is a true equation.
==========================================
Explanation:
The idea is that if we have
a/b = c/d
then that it is the same as
a*d = b*c
This is known as cross multiplication. We'll use this rule to get
15/12 = 4.5/3.6
15*3.6 = 12*4.5
54 = 54
We got the same value on both sides, meaning that the last equation is true. Consequently, it means the first equation is true as well (all three equations are true).
--------
You could also use your calculator to see that
15/12 = 1.25
4.5/3.6 = 1.25
showing that 15/12 = 4.5/3.6 is a true equation and the ratios form a proportion.
Answer:
15/12=4.5/3.6 = True
Step-by-step explanation:
Simplify the following: Left-hand
15/12
Hint: | Reduce 15/12 to lowest terms. Start by finding the GCD of 15 and 12.
The gcd of 15 and 12 is 3, so 15/12 = (3×5)/(3×4) = 3/3×5/4 = 5/4:
Answer: 5/4
______________________________
Approximate the following:
4.5/3.6
Hint: | Express 4.5/3.6 in decimal form.
4.5/3.6 = 1.25:
Answer: 1.25 = 5/4
Find the inverse of the following function.
Answer:
The inverse is 1/64 x^2 = y x ≥ 0
Step-by-step explanation:
f(x) = 8 sqrt(x)
y = 8 sqrt(x)
Exchange x and y
x = 8 sqrt (y)
Solve for y
Divide each side by 8
1/8 x = sqrt(y)
Square each side
(1/8 x)^2 = (sqrt(y))^2
1/64 x^2 = y
The inverse is 1/64 x^2 = y x ≥ 0
since x ≥0 in the original function
Answer:
[tex]\Huge \boxed{\mathrm{D}}[/tex]
Step-by-step explanation:
[tex]f(x)=8\sqrt{x}[/tex]
[tex]\sf Replace \ with \ y.[/tex]
[tex]y=8\sqrt{x}[/tex]
[tex]\sf Switch \ the \ variables.[/tex]
[tex]x= 8\sqrt{y}[/tex]
[tex]\sf Divide \ both \ sides \ of \ the \ equation \ by \ 8.[/tex]
[tex]\displaystyle \frac{x}{8} =\sqrt{y}[/tex]
[tex]\sf Square \ both \ sides \ of \ the \ equation.[/tex]
[tex]\displaystyle (\frac{x}{8} )^2 =y[/tex]
[tex]\displaystyle \frac{x^2 }{64} =y[/tex]
[tex]\displaystyle f^{-1}(x)=\frac{1}{64} x^2[/tex]
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The Width = 28 inches
The Height = 21 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3
Using Pythagoras Theorem
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 35²
We are given ratio: 4:3 as aspect ratio
Width = 4x
Height = 3x
(4x)² +(3x)² = 35²
= 16x² + 9x² = 35²
25x² = 1225
x² = 1225/25
x² = 49
x = √49
x = 7
Hence, for the 35 inch tv set
The Width = 4x
= 4 × 7
= 28 inches.
The Height = 3x
= 3 × 7
= 21 inches
Julissa gave out an equal number of oranges to each of the 6 apartments on her floor. if she gave each apartment 5 oranges, how many oranges did Julissa give out in all?
julissa gave equal oranges in 6 apartments
she gave each apartment 5 oranges
so total no. of oranges are = 6×5 = 30
Answer:
D. 30
Step-by-step explanation:
Jaclyn is one-fourth of a foot taller than John. John is 31/6 feet tall. How many feet tall is Jaclyn
Answer:
5 5/12
Step-by-step explanation:
31/6 feet + 1/4 foot
= 31/6 + 1/4
= [(31 * 4) / 6 * 4] + [(1 * 6) / 4 * 6]
= [ 124/24 ] + [ 6/24 ]
= (124 + 6) / 24
= 130 / 24
= 5 10/24
= 5 5/12
Hope this helps! Tell me if I'm wrong!
Solve for x -3x-3=-3(x+1)
Step-by-step explanation:
[tex] - 3x - 3 = - 3(x + 1) \\ - 3x - 3 = - 3x - 3 \\ - 3x + 3x = - 3 + 3 \\ 0 = 0[/tex]
Step 1: Use 3 to open the bracket
Step 2 : Collect like terms and simplify
Answer = 0
A slope triangle for line l is shown on the graph below. If the
slope of the line is 4/3 what is the value of w?
Answer:
9
Step-by-step explanation:
What we have to note is that the slope of a line is rise/run. This means that the amount of y change in that line is 4, and the amount of x change is 3.
We can now use a proportion to find the value of w.
[tex]\frac{4}{3} = \frac{12}{x}[/tex]
Cross multiply:
[tex]12\cdot36 = 36\\\\36\div4=9[/tex]
Hope this helped!
Answer: 9
Step-by-step explanation:
Which relation is a function?
The number two is a function
First rule of function: for each element of A there is one and only one element of B
For example, in the first one -5 is "collegated" to -2 and 3. So this isn't a function.
Naturally, every element of B can have more element of A
A low-noise transistor for use in computing products is being developed. It is claimed that the mean noise level will be below the 2.5-dB level of products currently in use. It is believed that the noise level is approximately normal with a standard deviation of .8. find 95% CI
Answer:
The 95% CI is [tex]2.108 < \mu < 2.892[/tex]
Step-by-step explanation:
From the question we are told that
The population mean [tex]\mu = 2.5[/tex]
The standard deviation is [tex]\sigma = 0.8[/tex]
Given that the confidence level is 95% then the level of confidence is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
=> [tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
here we would assume that the sample size is n = 16 since the person that posted the question did not include the sample size
So
[tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]
[tex]E = 0.392[/tex]
The 95% CI is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]
substituting values
[tex]2.108 < \mu < 2.892[/tex]
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 15 HCF of water is 32.84, and the cost for using 43 HCF is 79.04. What is the cost for using 36 HCF of water?
Answer:
67.49
Step-by-step explanation:
Let the number of HCF be x.
Let the cost be y.
You are given 2 points of a line: (15, 32.84) and (43, 79.04).
Now we find the equation of the line that passes through those points.
y - y1 = m(x - x1)
y - 32.84 = [(79.04 - 32.84)/(43 - 15)](x - 15)
y - 32.84 = (46.2/28)(x - 15)
y - 32.84 = 1.65(x - 15)
y = 1.65x - 24.75 + 32.84
y = 1.65x + 8.09
Now we let x = 36 and solve for y.
y = 1.65(36) + 8.09
y = 67.49
tan inverse 1/4 +tan inverse 2/7 = 1/2 cos inverse 3/5
Answer:
The equation is always false
Step-by-step explanation:
arctan1/4+arctan2/7=1/2arccos3/5
0.24497866+0.27829965=1/2(0.92729521)
0.52327832 =0.46364760
not equivalent and will never be.
For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is
Answer:
1.16
Step-by-step explanation:
Given that;
For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.
This implies that:
P(0<Z<z) = 0.3770
P(Z < z)-P(Z < 0) = 0.3770
P(Z < z) = 0.3770 + P(Z < 0)
From the standard normal tables , P(Z < 0) =0.5
P(Z < z) = 0.3770 + 0.5
P(Z < z) = 0.877
SO to determine the value of z for which it is equal to 0.877, we look at the
table of standard normal distribution and locate the probability value of 0.8770. we advance to the left until the first column is reached, we see that the value was 1.1. similarly, we did the same in the upward direction until the top row is reached, the value was 0.06. The intersection of the row and column values gives the area to the two tail of z. (i.e 1.1 + 0.06 =1.16)
therefore, P(Z ≤ 1.16 ) = 0.877
Brainliest for the correct answer!! A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.What is the line of best fit?A.y = –0.984x + 13.5B.y = –2.9x + 13.5C.–0.984 = –2.9x + 13.5D.y = 13.5x – 2.9
Answer:
B. y = –2.9x + 13.5
Step-by-step explanation:
You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is
y = a + bx, where a is the y intercept and b is the slope.
To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.
x y xy x²
1 . 11 = 11 → x² = 1² = 1
2 . 8 = 16 → x² = 2² = 4
3 . 4 = 12 → x² = 3² = 9
4 . 1 = 4 → x² = 4² = 16
5 . 0 = 0 → x² = 5² = 25
Total x = 1 + 2 + 3 + 4 + 5 = 15
Total y = 11 + 8 + 4+ 1 + 0 = 24
Sum of xy = 11 + 16 + 12 + 4 + 0 = 43
Sum of x² = 1 + 4 + 9 + 16 + 25 = 55
n = 5
So b = 5 (43) - (15) . (24) / 5 (55) - 15² = -2.9
a = y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5
Question
The point (-2,r) lies on the graph of 2x + y = 7 in the xy-plane. What is the value of r?
Answer: r = 11
Step-by-step explanation:
We know that the point (-2, r) lies on the graph of:
2*x + y = 7.
Then, if we that point is on the graph of the equation, we can replace the values and we will have:
2*(-2) + r = 7
and now we solve this for r-
-4 + r = 7
r = 7 + 4 = 11
r = 11
49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Group of answer choices
Answer:
Stratified Random sampling.
Step-by-step explanation:
As per the scenario, It is stratified random sampling as it divides students into strata which represent Sophomores, Juniors, and Seniors.
Simple random samples of the given sizes of the proportional to the size of the stratum which is to be taken from every stratum that is to be about 10 percent of students from every class that is selected here.
Hence, according to the given situation, the correct answer is a random stratified sampling.
if 2x-7 is 5 more than x+4, what is the value of 3x+5
Answer:
53
Step-by-step explanation:
Let's start with the given relation:
2x -7 = (x+4) +5
x = 16 . . . . . . . . . add 7-x
3x +5 = 3(16) +5 = 53 . . . . . multiply by 3 and add 5
The value of 3x+5 is 53.
Examine the two triangles. Are the triangles congruent? Justify your conclusions. If they are congruent, complete the following statement: "Yes, triangle __ congruent to triangle __ giving a detailed explanation of your reasoning. If they are not congruent, explain why you think so. Be specific in your answer and make sure to show your work.
Answer: The triangles are not congruent
==========================================
Explanation:
For triangle DEF, the missing angle D is
D+E+F = 180
D+80+60 = 180
D+140 = 180
D = 180-140
D = 40
While the missing angle K in triangle JKL is
J+K+L = 180
80+K+50 = 180
K+130 = 180
K = 180-130
K = 50
---------------------
The three angles for triangle DEF are
D = 40E = 80F = 60The three angles for triangle JKL are
J = 80K = 50L = 50We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.
The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.
Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.
The price of a technology stock was $ 9.56 yesterday. Today, the price rose to $ 9.69 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer and Step-by-Step explanation:
% increase = 100 x [(new price) - (original price)] / (original price)] = 100 (9.67 - 9.56) / 9.56
% increase ≅ 1.2% (to the nearest tenth)
A special mixed-nut blend at a store cost $1.35 per lb, and in 2010 the blend cost $1.83 per lb. Let y represent the cost of a pound of the mixed-nut blend x years after 2005. Use a linear equation model to estimate the cost of a pound of the mixed-nut blend in 2007.
Answer:
y = $1.542 per lb
Step-by-step explanation:
given data
mixed-nut blend store cost 2005 = $1.35 per lb
blend cost in 2010 = $1.83 per lb
solution
we consider here y = cost of a pound
and x year = after 2005
we will use here linear equation model
so
[tex]\frac{y - 1.35}{1.83-1.35} = \frac{x-10}{5 - 0}[/tex] .........................1
solve it we get
5y - 6.75 = .48 x
so
at 2007 year here x wil be 2
so
[tex]y = \frac{0.48 \times 2 + 6.75}{5}[/tex]
solve it we get
y = $1.542 per lb
Lydia drives from city a to city b to transport goods. her return speed is 3 times her departure speed and she takes 40 minutes less on her return trip. how long did her departure trip take?
Answer:
1 hour
Step-by-step explanation:
Hello, let's say that her departure trip takes t in minutes, as her return speed is 3 times her departure speed, she took t/3 for the return and we know that this 40 minutes less, so we can write.
t/3=t-40
We can multiply by 3
t = 3t -40*3 = 3t - 120
This is equivalent to
3t -120 = t
We subtract t
2t-120 = 0
2t = 120
We divide by 2
t = 120/2 = 60
So this is 60 minutes = 1 hour.
Thank you.
A recent survey of 1090 U.S. adults selected at random showed that 623 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.
Answer:
0.572
Step-by-step explanation:
From the question,
We have
n = 1090 of US adults
x = 623 selected from this population at random who consider the occupation to be one of great prestige
So we have that
The probability of X = x/n
= 623/1090
= 0.572
We conclude that 0.572 is the probability that a US adult selected at random thinks the occupation has great prestige.
Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x)=-2cos^(2)x
Answer:
Increasing
0°≤x≤180°
Decreasing
180°≤x≤360°
Each leg of a 45°-45°-90° triangle measures 12 cm.
What is the length of the hypotenuse?
Z
х
45°
45°
O 6 cm
12 cm
12 cm
O 672 cm
O 12 cm
O 122 cm
Answer:
The legs are 12 cm each, so the hypotenuse is
√(144+144)=12√2
Step-by-step explanation:
Applying the Pythagorean Theorem, the length of the hypotenuse is: 12√2 cm.
The Pythagorean TheoremWhere, a and b are two legs of a right triangle, and c is the hypotenuse, the Pythagorean Theorem states that, c² = a² + b².Given the two legs of the right triangle to be 12 cm
Therefore:c² = 12² + 12².
c² = 288
c = √288
c = 12√2 cm
Therefore, applying the Pythagorean Theorem, the length of the hypotenuse is: 12√2 cm.
Learn more about, the Pythagorean Theorem on:
https://brainly.com/question/654982
A number is chosen at random from the set of consecutive natural numbers $\{1, 2, 3, \ldots, 24\}$. What is the probability that the number chosen is a factor of $4!$? Express your answer as a common fraction.
Answer:
[tex]Probability = \frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]Set:\ \{1, 2, 3, \ldots, 24\}[/tex]
[tex]n(Set) = 24[/tex]
Required
Determine the probability of selecting a factor of 4!
First, we have to calculate 4!
[tex]4! = 4 * 3 * 2 * 1[/tex]
[tex]4! = 24[/tex]
Then, we list set of all factors of 24
[tex]Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}[/tex]
[tex]n(Factors) = 8[/tex]
The probability of selecting a factor if 24 is calculated as:
[tex]Probability = \frac{n(Factor)}{n(Set)}[/tex]
Substitute values for n(Set) and n(Factors)
[tex]Probability = \frac{8}{24}[/tex]
Simplify to lowest term
[tex]Probability = \frac{1}{3}[/tex]
Find the area of the irregularly-shaped hexagon below
let each box length be 1
for white triangle
area = ½bh
=½(4)(2)
=4
for orange triangle
area=½(2)(3)
=3
for blue marked boxes
each of the box
area=l²
=(1)²
=1
there are 16 boxes
so the total area will be 16
total area of the hexagon = 4+3+16
=23 square units
[tex]A_1=\dfrac{1}{2}(3+5)\cdot 3=12\\A_2=1\cdot5=5\\A_3=\dfrac{1}{2}(5+1)\cdot 2=6[/tex]
So the area of the whole shape is [tex]12+5+6=23[/tex]
Which of the following is NOT a requirement of testing a claim about two population means when 1 and 2 are unknown and not assumed to be equal? Choose the correct answer below. A. The two samples are dependent. B. Both samples are simple random samples. C. Either the two sample sizes are large (30 and 30) or both samples come from populations having normal distributions, or both of these conditions are satisfied. D. The two samples are independent.
Answer:
b
Step-by-step explanation:
Techwiz electronics makes a profit of $35 for each mp3 and $18 for each DVD last week techwiz sold a combined total of 118 mp3 and DVD players. Let x be the number of mp3 sold last week write an expression for the combined total profit (in dollars) made last week
Answer:
The total profit is [tex]p = 17x + 2124[/tex]
Step-by-step explanation:
From the question we are told that
The profit made on each mp3 is k = $35
The profit made on each mp3 is y = $18
The total amount sold is n = 118
Now given that the amount of mp3 sold is x then the amount of DVD sold is mathematically evaluated as
[tex]n - x[/tex]
Now the profit made on the x number of mp3 sold is
[tex]x * 35 = 3x[/tex]
And the the profit made from the n-x number of DVD sold is 18 (n-x ) = 18 - 18x
So the total profit made last week from the sales of both mp3 and DVD is
[tex]p = 35x + 18n - 18x[/tex]
[tex]p = 17x + 18(118)[/tex]
[tex]p = 17x + 2124[/tex]
If (x - 2) and (x + 1) are factors of
x + px? + qx + 1, what is the sum of p and q?
Answer:
p + q = -3
Step-by-step explanation:
First we need to take the original equation, and factor it to a form that's easier to get two binomial factors from (i.e., let's get a quadratic):
x^3 + px^2 + qx + 1
= x (x^2 + px + q) + 1
Now that we have factored out the x, we have a quadratic trinomial which we know can be broken down into two linear binomials. The problem gives us two linear binomials, so let's take a look.
(x - 2) (x + 1) = (x^2 + px + q)
x^2 - 2x + x -2 = x^2 + px + q
Now let's solve.
x^2 - x - 2 = x^2 + px + q
-x - 2 = px + q
From here, we can easily see that p = -1 (the coefficient of x) and q = -2.
Hence, p + q = -1 + -2 = -3.
Cheers.
Simplify . 7+ the square root of 6(3+4)-2+9-3*2^2 The solution is
Answer:
7+sqrt(37)
Step-by-step explanation:
7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)
What is the simplified form of x minus 5 over x squared minus 3x minus 10⋅ x plus 2 over x squared plus x minus 12 ? (6 points) Select one: a. 1 over the quantity x minus 3 times the quantity x plus 4 b. 1 over the quantity x minus 3 times the quantity x plus 2 c. 1 over the quantity x plus 4 times the quantity x minus 5 d. 1 over the quantity x plus 2 times the quantity x minus 5
Answer:
[tex]\ \text{a. }\quad\dfrac{1}{(x-3)(x+4)}[/tex]
Step-by-step explanation:
Maybe you want the product ...
[tex]\dfrac{x-5}{x^2-3x-10}\cdot\dfrac{x+2}{x^2+x-12}=\dfrac{x-5}{(x-5)(x+2)}\cdot\dfrac{x+2}{(x-3)(x+4)}\\\\=\boxed{\dfrac{1}{(x-3)(x+4)}}[/tex]
__
Numerator factors of (x-5) and (x+2) cancel those in the denominator.
Solve systems of equations 15 points NOT CLICKBAIT!!! -6y+11y= -36 -4y+7x= -24
Answer:
x = -264/35
y = -36/5
Step-by-step explanation:
-6y + 11y = -36
-4y + 7x = -24
Solve for y in the first equation.
-6y + 11y = -36
Combine like terms.
5y = -36
Divide both sides by 5.
y = -36/5
Plug y as -36/5 in the second equation and solve for x.
-4(-36/5) + 7x = -24
Expand brackets.
144/5 + 7x = -24
Subtract 144/5 from both sides.
7x = -264/5
Divide both sides by 7.
x = -264/35
Answer: -264/35
Step-by-step explanation:
i did my work on a calculator
