Answer:
[tex]\frac{41}{28}[/tex] = [tex]1\frac{13}{28}[/tex]
Step-by-step explanation:
In order to add fractions, the denominators must all be the same value (the lowest common denominator). The lowest common denominator is the smallest value that all of the given denominators (in this case, the denominators are 4, 14, and 7) can divide into.
Here, the smallest number that all three of the given denominators can perfectly divide into is 28:
28 ÷ 4 = 7
28 ÷ 14 = 2
28 ÷ 7 = 4
Therefore, our lowest common denominator is 28.
The next step is to change our numerators to match our lowest common denominator. To do this, we have to multiply the numerator by the same value that we would need to multiple the denominator by in order to get our lowest common denominator.
For our first term of 1/4, we need to multiply our denominator (4) by 7 in order to get our lowest common denominator of 28. So, we need to also multiply our numerator by 7:
[tex]\frac{1}{4}[/tex] × [tex]\frac{7}{7}[/tex] = [tex]\frac{7}{28}[/tex]
Therefore, our first term becomes [tex]\frac{7}{28}[/tex].
For our second term of 5/14, we need to multiply our denominator (14) by 2. So, we need to also multiply our numerator by 2:
[tex]\frac{5}{14}[/tex] × [tex]\frac{2}{2}[/tex] = [tex]\frac{10}{28}[/tex]
Therefore, our second term becomes [tex]\frac{10}{28}[/tex].
For our third term of 6/7, we need to multiply our denominator (7) by 4. So, we need to also multiply our numerator by 4:
[tex]\frac{6}{7}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{24}{28}[/tex]
Therefore, our third term becomes [tex]\frac{24}{28}[/tex].
Now that they all have the same denominator, we simply have to add all three together:
[tex]\frac{7}{28}[/tex] + [tex]\frac{10}{28}[/tex] + [tex]\frac{24}{28}[/tex] = [tex]\frac{41}{28}[/tex]
When we simplify this into a mixed number, we get:
[tex]\frac{41}{28}[/tex] = [tex]1\frac{13}{28}[/tex]
Answer:
41/28 = 1 (13/28)
Step-by-step explanation:
gotta make the denominators the same.
Which of the following exponential equations is equivalent to the logarithmic
equation below?
log 970 = x
A.x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X
Given:
The logarithmic equation is:
[tex]\log 970=x[/tex]
To find:
The exponential equations that is equivalent to the given logarithmic equation.
Solution:
Property of logarithm:
If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]
We know that the base log is always 10 if it is not mentioned.
If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]
We have,
[tex]\log 970=x[/tex]
Here, base is 10 and the value of a is 970. By using the properties of exponents, we get
[tex]970=10^x[/tex]
Interchange the sides, we get
[tex]10^x=970[/tex]
Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].
Note: It should be "=" instead of "-" in option B.
Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are needed? Round to the nearest tenth.
Answer:
3.1 gallons
Step-by-step explanation:
To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that
miles of gas / gallons = miles of gas / gallons
23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house
If we write the gallons needed to go to Bob's mother's house as g, we can say
23 miles / 1 gallon = 72 miles/g
multiply both sides by 1 gallon to remove a denominator
23 miles = 72 miles * 1 gallon /g
multiply both sides by g to remove the other denominator
23 miles * g = 72 miles * 1 gallon
divide both sides by 23 miles to isolate the g
g = 72 miles * 1 gallon/23 miles
= 72 / 23 gallons
≈ 3.1 gallons
What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)
Answer: A (x+1)(x+2)(x+5)
Step-by-step explanation:
When Cameron moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 24 inches tall and Tree B was 39 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
Answer:
time interval when Tree A is taller than Tree B is;
t > 5 years
Step-by-step explanation:
Tree A;
Initial height = 24 inches
Increase in height per year = 6 inches per year
Thus, for t years after being planted, height is;
A = 6t + 24
Tree B;
Initial height = 39 inches
Increase in height per year = 3 inches per year
Thus, for t years after being planted, height is;
B = 3t + 39
For tree A to be taller than tree B, then it means thay;
A > B
Thus;
6t + 24 > 3t + 39
Subtract 3t from both sides to get;
6t - 3t + 24 > 39
3t + 24 > 39
3t > 39 - 24
3t > 15
Divide both sides by 3 to get;
t > 5
Thus, time interval when Tree A is taller than Tree B is; t > 5
Which table represents a relation that's a non-function?
Answer:
The table in the attachment is the right option
Step-by-step explanation:
A table that represents a function must have exactly one y-value assigned to every x-value. In other words, a table that is a function cannot have any x-value (input) with two corresponding different y-values (outputs).
The table in the attachment below represents a relation that is non-function because it has two outputs, 5 and 7, that are assigned or corresponding to one input, 7.
According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50 and that a sample of 30 theaters was randomly selected. What is the probability that the sample mean will be between $7.75 and $8.20
Answer:
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
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 normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.
This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]
Sample of 30:
This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]
What is the probability that the sample mean will be between $7.75 and $8.20?
This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.
X = 8.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = 2.63[/tex]
[tex]Z = 2.63[/tex] has a p-value of 0.9957
X = 7.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = -2.3[/tex]
[tex]Z = -2.3[/tex] has a p-value of 0.0107.
0.9957 - 0.0157 = 0.985
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
What is the measure of F?
G
65
10
H H
10
A. Cannot be determined
B. 55
C. 75
D65
Answer:
D. 65°
Step-by-step explanation:
It is so because the triangle is isosceles, two identical sides and two equal angles.
HELP!!!!!!!!!!! SOMEONE PLEASE HELP!!!
For the graph below, which of the following is a possible function for h?
A) h(x) = 4-x
B) h(x) = 2x
C) h(x) = 5x
D) h(x) = 3x
9514 1404 393
Answer:
C) h(x) = 5^x
Step-by-step explanation:
h(x) is shown on the graph as having the highest rate of growth. That means, relative to the other functions, the base of the exponential is larger. Of the choices offered, the one with the largest growth factor is ...
h(x) = 5^x
_____
The general form of an exponential function is ...
f(x) = (initial value) · (growth factor)^x
What is the value of x in the triangle? 45, 45, x
Answer:
90
Step-by-step explanation:
it its a 45 45 90 triangle
Can you help me please,
?
Solve the equation by completing the square.
0 = 4x2 − 72x
Answer:
B
Step-by-step explanation:
Given
4x² - 72x = 0 ← factor out 4 from each term
4(x² - 18x) = 0
To complete the square
add/subtract (half the coefficient of the x- term)² to x² - 18x
4(x² + 2(- 9)x + 81 - 81) = 0
4(x - 9)² - 4(81) = 0
4(x - 9)² - 324 = 0 ( add 324 to both sides )
4(x - 9)² = 324 ( divide both sides by 4 )
(x - 9)² = 81 ( take the square root of both sides )
x - 9 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 9 to both sides )
x = 9 ± 9
Then
x = 9 - 9 = 0
x = 9 + 9 = 18
Answer:0,18
Step-by-step explanation:
its right
1. Write a variable expression that matches the following situation: Marguerite wants to put a garland around her garden. If the length of the garden is 50 meters and the width of the garden is 2 more than the length, what is the perimeter of the garden?
Answer:
3x2,−23y,√5m, 3 x 2 , − 2 3 y , 5 m
Step-by-step explanation:
that is the answer i think
While out for a run, two joggers with an average age of 55 are joined by a group of three more joggers with an average age of m. if the average age of the group of five joggers is 45, which of the following must be true about the average age of the group of 3 joggers?
a) m=31
b) m>43
c) m<31
d) 31 < m < 43
Answer:
they have it on calculator soup
Step-by-step explanation:
Answer:
D. 31<m<43
Step-by-step explanation:
45 x 5 = 225 which is the age of the 5 joggers altogether.
55 x 2 = 110 which is the age of the 2 joggers together.
3m + 110 = 225 then solve for m so,
3m = 115
m = 38.3333
so hence, m is greater than 31 but less than 43.
answer: D
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1=50 n2=35
x¯1=13.6 x¯2=11.6
σ1=2.2 σ2=3.0
Required:
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
Answer:
a. 2
b. The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
[tex]\mu_1 = 13.6, s_1 = \frac{2.2}{\sqrt{50}} = 0.3111[/tex]
Sample 2:
[tex]\mu_2 = 11.6, s_2 = \frac{3}{\sqrt{35}} = 0.5071[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 13.6 - 11.6 = 2[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.3111^2+0.5071^2} = 0.595[/tex]
a. What is the point estimate of the difference between the two population means?
Sample difference, so [tex]\mu = 2[/tex]
b. Provide a 90% confidence interval for the difference between the two population means.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
The margin of error is:
[tex]M = zs = 1.645(0.595) = 0.98[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 0.98 = 1.02
The upper end of the interval is the sample mean added to M. So it is 2 + 0.98 = 2.98
The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. Provide a 95% confidence interval for the difference between the two population means.
Following the same logic as b., we have that [tex]Z = 1.96[/tex]. So
[tex]M = zs = 1.96(0.595) = 1.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 1.17 = 0.83
The upper end of the interval is the sample mean added to M. So it is 2 + 1.17 = 3.17
The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
what is the solution to the equation?
Answer:
Step-by-step explanation:
log(20x³) - 2logx = 4
log(20x³) -log(x²) = 4
log(20x³/x²) = 4
log(20x) = 4
20x = 10⁴
x = 10⁴/20 = 500
X+34>55
Solve the inequality and enter your solution as an inequality comparing the variable to a number
Answer:
x > 21
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 34 > 55
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 34 on both sides: x > 21Consider A Triangle ABC. Suppose That A= 119 Degrees, B=53, And C=57. Solve The Traingle
9514 1404 393
Answer:
a = 94.8, B = 29.3°, C = 31.7°
Step-by-step explanation:
Side 'a' can be found using the Law of Cosines:
a² = b² +c² -2bc·cos(A)
a = √(2809 +3249 -6042·cos(119°)) ≈ √8987.22 ≈ 94.8
Then one of the other angles can be found from the Law of Sines.
sin(C)/c = sin(A)/a
C = arcsin(c/a·sin(A)) ≈ arcsin(0.525874) ≈ 31.7°
Then the remaining angle can be found to be ...
B = 180° -A -C = 180° -119° -31.7° = 29.3°
__
The solution is a ≈ 94.8, B ≈ 29.3°, C ≈ 31.7°.
An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it take both pipes to fill the pool?
Answer:
It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
Step-by-step explanation:
Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:
1/5 + 1/4 = X
0.20 + 0.25 = X
0.45 = X
9/20 = X
9 = 60
2 = X
120/9 = X
13,333 = X
Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
!!!!Please Answer Please!!!!
ASAP!!!!!!
!!!!!!!!!!!!!
Answer:
False
Step-by-step explanation:
well i think that the answer from my calculations
I need help understanding how to get the answer.
Answer:
-157.87
Step-by-step explanation:
1) the rules are:
[tex]log_a(bc)=log_ab+log_ac;[/tex]
and
[tex]log_ab^c=c*log_ab.[/tex]
2) according to the rules above:
[tex]log_7(yz^8)=log_7y+8log_7z=-6.19-8*18.96=-157.87.[/tex]
The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations. –9 –1 0 1
9514 1404 393
Answer:
(b) -1
Step-by-step explanation:
The graph shows the difference between the two expressions is zero at x=-1.
__
Additional comment
For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.
Answer:
The answer is b: -1
Step-by-step explanation:
good luck!
Please see attached for the question. The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1400 and the standard deviation is $95.
Answer:
1. 2.1%
2. 47.7%
3. 68.2%
4. 34.1%
5. 49.9%
6. 0.1%
These values may be rounded differently depending on set rounding limits.
Pleas help me in this question Find R
Answer:
R = 25.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos R = adj side / hyp
cos R = 9/10
Taking the inverse cos of each side
cos ^-1 ( cos R) = cos^ -1 ( 9/10)
R=25.84193
Rounding to the nearest tenth
R = 25.8
Answer:
[tex]\boxed {\boxed {\sf D. \ 25.8 \textdegree} }[/tex]
Step-by-step explanation:
We are asked to find the measure of an angle given the triangle with 2 sides. This is a right triangle because of the small square representing a right angle. Therefore, we can use trigonometric functions. The three major functions are:
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacentWe are solving for angle R, and we have the sides TR (measures 9) and SR (measures 10).
The side TR (9) is adjacent or next to angle R. The side SR (10) is the hypotenuse because it is opposite the right angle.We have the adjacent side and the hypotenuse, so we will use the cosine function.
[tex]cos \theta = \frac {adjacent}{hypotenuse}[/tex]
[tex]cos R = \frac {9}{10}[/tex]
Since we are solving for an angle, we must take the inverse cosine of both sides.
[tex]cos^{-1}(cos R) = cos ^{-1} ( \frac{9}{10})[/tex]
[tex]R = cos ^{-1} ( \frac{9}{10})[/tex]
[tex]R= 25.84193276[/tex]
If we round to the nearest tenth, the 4 in the hundredth place tells us to leave the 8 in the tenths place.
[tex]R \approx 25.8 \textdegree[/tex]
The measure of angle R is approximately 25.8 degrees and choice D is correct.
An equation is shown below:
3(4x − 2) = 1
Which of the following correctly shows the steps to solve this equation?
Step 1: 12x − 2 = 1; Step 2: 12x = 3
Step 1: 12x − 6 = 1; Step 2: 12x = 7
Step 1: 7x + 1 = 1; Step 2: 7x = 0
Step 1: 7x − 5 = 1; Step 2: 7x = 6
Step-by-step explanation:
Step 1: 12x-6= 1
step 2:12x=7
Which of the following is the differnce of two squares
A group of rowdy teenagers near a wind turbine decide to place a pair of pink shorts on the tip of one blade, they notice the shorts are at its maximum height of 16 meters at a and it’s minimum height of 2 meters at s.
Determine the equation of the sinusoidal function that describes the height of the shorts in terms of time.
Determine the height of the shorts exactly t=10 minutes, to the nearest tenth of a meter
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
Question: The likely missing parameters in the question are;
The time at which the shorts are at the maximum height, t₁ = 10 seconds
The time at which the shorts are at the minimum height, t₂ = 25 seconds
The general form of a sinusoidal function is A·sin(B(x - h)) + kWhere;
A = The amplitude
The period, T = 2·π/B
The horizontal shift = h
The vertical shift = k
The parent equation of the sine function = sin(x)
We find the values of the variables, A, B, h, and k as follows;
The given parameters of the sinusoidal function are;
The maximum height = 16 meters at time t₁ = 10 seconds
The minimum height = 2 meters at time t₂ = 25 seconds
The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)
∴ T = 2 × (25 - 10) = 30
The amplitude, A = (Maximum height- Minimum height)/2
∴ A = (16 m - 2 m)/2 = 7 m
The amplitude of the motion, A = 7 meters
T = 2·π/B
∴ B = 2·π/T
T = 30 seconds
∴ B = 2·π/30 = π/15
B = π/15
At t = 10, y = Maximum
Therefore;
sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2
Plugging in B = π/15, and t = 10, gives;
((π/15)·(10 - h)) = π/2
10 - h = (π/2) × (15/π) = 7.5
h = 10 - 7.5 = 2.5
h = 2.5
The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A
Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7
The given minimum value = 2
The vertical shift, k = 2 - (-7) = 9
Therefore, k = 9
Therefore;
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
More can be learned about sinusoidal functions on Brainly here;
https://brainly.com/question/14850029
Graph the inequality.
7 <= y - 2x < 12
Answer:
X(-12,-7)
Step-by-step explanation:
This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.
Which function describes this graph? (CHECK PHOTO FOR GRAPH)
A. y = x^2 + 7x+10
B. y = (x-2)(x-5)
C. y = (x + 5)(x-3)
D.y = x^2+5x+12
Answer:
Option A. y = x² + 7x + 10
Step-by-step explanation:
We'll begin calculating the roots of the equation from the graph.
The roots of the equation on the graph is where the curve passes through the x-axis.
The curve passes through the x-axis at –5 and –2
Next, we shall determine the equation. This can be obtained as follow:
x = –5 or x = –2
x + 5 = 0 or x + 2 = 0
(x + 5)(x + 2) = 0
Expand
x(x + 2) + 5(x + 2) = 0
x² + 2x + 5x + 10 = 0
x² + 7x + 10 = 0
y = x² + 7x + 10
Thus, the function that describes the graph is y = x² + 7x + 10
the point (-2,5) is reflected across the y-axis. which of these is the ordered pair of the image
Answer:(2,5)
Step-by-step explanation: watch this video
https://youtu.be/l78P2Xi68-k
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
PLEASE HELP
Answer:
8
Step-by-step explanation:
As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8
