PLEASE HELP!! Solve this logarithmic equation for the value of the variable. Be sure to check for extraneous solutions
Answers
Step-by-step explanation:
log(5x) - log(2) = log(5x/2)
therefore,
log(4x - 1) = log(5x/2)
4x - 1 = 5x/2
8x - 2 = 5x
3x - 2 = 0
3x = 2
x = 2
since this is basically a linear equation in x, there is only one solution, and that is x = 2.
for x = 2 all arguments of the log functions are positive.
4x - 1 = 4×2 - 1 = 8 - 1 = 7
5x = 5×2 = 10
these are all valid arguments for the log function.
so, x = 2 is a valid and not extraneous solution.
Related Questions
what is one macroeconomic problem that could cause the federal reserve to become aggressive in raising interest rates?
Answers
One macroeconomic problem that could cause the Federal Reserve to become aggressive in raising interest rates is inflation.
Inflation is the increase in the prices of goods and services over time, which erodes the purchasing power of money. When inflation is high, people tend to spend less and save more, which slows down economic growth.
In response to high inflation, the Federal Reserve may raise interest rates to tighten monetary policy and reduce spending. Higher interest rates make borrowing more expensive, which reduces the amount of money people have to spend. Additionally, higher interest rates make saving more attractive, which encourages people to save more and spend less. By raising interest rates, the Federal Reserve can control inflation and prevent it from becoming too high. However, raising interest rates can also have negative effects on the economy, such as slowing down investment and reducing consumer spending. Therefore, the Federal Reserve must carefully consider the balance between controlling inflation and maintaining economic growth when making decisions about interest rates.Know more about the Inflation
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the assumptions going into the model are that: a. the mean value of the number of disasters at a given temperature rise is linear in temperature rise b. the actual number of disasters is approximately normally distributed around its mean with a constant variance. the true value that was left out was 16, use the standard error of prediction (the stuff in the square root in the prediction interval) and the prediction from the regression line to calculate a t statistic. what is the pvalue for the null hypothesis that the point belongs to this line under these
Answers
Based on the given assumptions, we can assume that the model predicts the number of disasters at a given temperature rise linearly. However, it is important to note that this model is based on certain assumptions that may or may not be accurate.
These assumptions include the mean value being linear in temperature rise and the actual number of disasters being normally distributed with constant variance.
Given the true value of 16 that was left out, we can use the standard error of prediction and the prediction from the regression line to calculate a t statistic. The null hypothesis is that the point belongs to this line under these assumptions.
To calculate the t statistic, we can use the formula:
t = (observed value - predicted value) / standard error of prediction
Using the given information, we can calculate the t statistic as:
t = (16 - predicted value) / standard error of prediction
Once we have the t statistic, we can calculate the p-value using a t-distribution table or a statistical software. The p-value represents the probability of getting a t statistic as extreme or more extreme than the one we calculated under the null hypothesis.
Based on the p-value, we can determine if we reject or fail to reject the null hypothesis. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that the point does not belong to the line. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the point belongs to the line.
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the term to term rule of a sequence is add 7 then multiply by 2, the third term of the sequence is 17, work out the second term of the sequence
Answers
The second term of the sequence is given as follows:
1.5.
How to obtain the second term of the sequence?We use a recursive rule for the sequence, as we have the rule to obtain the (n + 1)th term considering the nth term.
The (n+1)th term rule of a sequence is add 7 then multiply by 2, hence the recursive formula is given as follows:
[tex]a_{n+1} = 2(a_n + 7)[/tex]
The third term for this problem is given as follows:
[tex]a_3 = 17[/tex]
Hence the second term is obtained as follows:
[tex]a_{3} = 2(a_2 + 7)[/tex]
[tex]2a_2 + 14 = 17[/tex]
[tex]2a_2 = 3[/tex]
[tex]a_2 = 1.5[/tex]
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what is the area of a rooftop garden
Answers
The area of the garden is 272 ft².
We have,
The garden has two shapes:
Rectangle and a triangle.
Now,
Length = 12 ft
Width = 20 ft
Area of the rectangle.
= Length x Width
= 12 x 20
= 240 ft²
And,
Base = 8 ft
Height = (20 - 12) = 8 ft
Area of the triangle.
= 1/2 x base x height
= 1/2 x 8 x 8
= 32 ft²
Now,
Area of the garden.
= 240 + 32
= 272 ft²
Thus,
The area of the garden is 272 ft².
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find t_{5}(x), the degree 5 taylor polynomial of the function f(x)= \cos(x) at a = 0.
Answers
the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.
What is Taylor series?
The Taylor series is a representation of a function as an infinite sum of terms involving the function's derivatives at a particular point. It provides a way to approximate a function with a polynomial expression.
To find the degree 5 Taylor polynomial, denoted as T₅(x), of the function f(x) = cos(x) at a = 0, we need to compute the polynomial using the derivatives of f evaluated at x = 0.
The Taylor polynomial of degree n for a function f(x) centered at a is given by:
Tₙ(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + ... + (fⁿ(a)/n!)(x - a)ⁿ
In this case, a = 0, so the Taylor polynomial simplifies to:
T₅(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + (f⁴(0)/4!)x⁴ + (f⁵(0)/5!)x⁵
Now, let's calculate the derivatives of f(x) = cos(x) up to the 5th order:
f'(x) = -sin(x)
f''(x) = -cos(x)
f'''(x) = sin(x)
f⁴(x) = cos(x)
f⁵(x) = -sin(x)
Evaluating these derivatives at x = 0:
f(0) = cos(0) = 1
f'(0) = -sin(0) = 0
f''(0) = -cos(0) = -1
f'''(0) = sin(0) = 0
f⁴(0) = cos(0) = 1
f⁵(0) = -sin(0) = 0
Substituting these values into the Taylor polynomial formula:
T₅(x) = 1 + 0x + (-1/2!)x² + (0/3!)x³ + (1/4!)x⁴ + (0/5!)x⁵
Simplifying the expression:
T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴
Therefore, the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.
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a camper lights an oil lantern at noon and lets it burn continuously. once the lantern is lit, the lantern burns oil at a constant rate each hour. at p.m., the amount of oil left in the lantern is ounces. at p.m., the amount of oil left in the lantern is ounces. based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at noon?
Answers
There were 16 ounces of oil in the lantern at noon.
Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.
We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:
x - rt = y
where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:
x - 2r = 12
And at 4 pm:
x - 4r = 8
Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:
2r = 4
r = 2
Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:
x - 2(2) = 12
x - 4 = 12
x = 16
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Angle D of △DEF is congruent to ∠G of △GHJ. Angle E is congruent to ∠H. Side DE is congruent to side HJ. Can you prove that the two triangles are congruent? Explain your answer.
No image attached.
Answers
Answer:
No
Step-by-step explanation:
"Looking" at our triangles
If Angle D is congruent to Angle G, and angle E is congruent to Angle H, lets call those the first and second vertices of each triangle. If we're trying to prove the triangles congruent, we're trying to prove Triangle DEF is congruent to Triangle GHJ (in that order, since we're already given that the first and second angles correspond between triangles).
Could these triangle be congruent? Yes! As a quick example, imagine two Equilateral triangles with side lengths 5. They are congruent, and they do have the first angle and second angle corresponding pairs congruent, and one of those sides from triangle 1 does match the length of one of the sides in triangle 2. ...and they are congruent triangles.
The problem with the given scenario is that the side they give for triangle 1 (between vertex 1 and 2) is not the corresponding side of triangle 2 (between vertex 2 and 3). This makes it so that we cannot guarantee that the triangles are congruent.
As can be seen in the attached image, I've made Side DE length 2, and put it on a coordinate plane so it's easy to see. Side HJ is also definitely length 2. Clearly, those triangles are not congruent.
When would triangles be congruent?
Going back to the definition of congruent triangles, three corresponding angles and three corresponding sides must be congruent. That's 6 pairs of parts needed to be proven congruent to prove triangles congruent!
Fortunately, there are a number of theorems that can be proven to lessen the amount of pairs of parts needed to be proven congruent and still guarantee that the resulting triangles must be congruent.
There are exactly 5 cases:
SSSSASASAAASHLIt looks like a bunch of alphabet soup, but notice that all of them require 3 pieces of information (even HL, which is Hypotenuse-Leg... since there's a Hypotenuse, it must be a right triangle, so there are a pair of corresponding congruent right angles that are congruent that they don't talk about)
In order to remember which items work, remember that you MUST know 3 parts, and think about all of the way you could know 3 parts:
Scenario 1: Have all 3 side pairs (SSS)
There is only one way that all three sides can be equal, and yes, that is one of the triangle congruence shortcuts.
Scenario 2: Have 2 side pairs & 1 angle pair
There are two option here.
two sides and the angle between them (SAS), ortwo sides and an angle NOT between them (...nope).Two sides with the angle between them is SAS (note the angle is between them).
Two sides with the angle not between them is ... (well, that can get you in trouble). Conveniently, that is NOT one of the triangle congruence theorems. So, stay out of trouble, and don't use this for triangle congruence.
Interestingly, HL, is a special case of this "trouble case". Note that if you have the Hypotenuse and a leg, that's two Sides. The right Angle is NOT the angle between those two sides (because the hypotenuse is always across from the right angle). When that angle is 90 degrees, then the set of two sides and the angle not between them DOES work as sufficient to prove triangle congruence, and it's the only time that it's sufficient.
Scenario 3: Have 1 Side and 2 Angles
Again, there are two option here:
two Angles and the Side between them (ASA), ortwo Angles and a Side NOT between them (AAS).In either scenario, this is sufficient to prove the triangles are congruent.
Scenario 4: Have all 3 angles (AAA)
This definitely won't be enough to prove congruence. Zoom in. It's got the same angles, but not the same lengths.
So, only 5 short ways to prove triangles are congruent, and all of them require 3 parts of one triangle corresponding to 3 parts of another, each of the 3 pairs must be congruent.
due sometime very soon
Answers
Answer:
D. Yes
Step-by-step explanation:
if you use a level of significance in a two-tail hypothesis test, what decision will you make if zstat= 1.58?
Answers
If a level of significance is used in a two-tail hypothesis test, and zstat= 1.58, we will fail to reject the null hypothesis.
In a two-tail hypothesis test, we test for the possibility of the sample mean being significantly different from the population mean in both directions, i.e., in both tails of the normal distribution. The level of significance is the probability of rejecting the null hypothesis when it is true. If the calculated test statistic (in this case, zstat= 1.58) falls outside the critical region, i.e., the region of rejection, then we fail to reject the null hypothesis. In other words, we cannot conclude that the sample mean is significantly different from the population mean. Therefore, the correct decision in this case is to fail to reject the null hypothesis.
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Suppose years of schooling, s, is the only variable that affects earnings. The equations for the weekly salaries of male and female workers are given by: wm = 500 + 100s and wf = 300 + 75s. On average, men have 14 years of schooling and women have 12 years of schooling. (a) What is the male-female wage differential in the labor market? The wage differential can be written as: )75300(100500 fsmsfwmww = 500 + 100(14) – 300 – 75(12) = $700. (b) Using the Oaxaca decomposition, calculate how much of this wage differential is due to discrimination?
Answers
Wage differential is due to discrimination = 700 - 700 = 0 .The Oaxaca decomposition is a method used to estimate the portion of the wage differential between two groups (in this case, male and female workers) that can be attributed to discrimination.
The decomposition breaks down the wage differential into two components: the explained component and the unexplained component.The explained component represents the portion of the wage differential that can be attributed to differences in observable characteristics between the two groups, such as years of schooling.
The unexplained component represents the portion of the wage differential that cannot be explained by observable characteristics and is often interpreted as the component related to discrimination or unobserved factors.
To calculate the Oaxaca decomposition, we need to follow these steps:
Step 1: Calculate the average wage of male workers (wm) and female workers (wf) using the given equations:
wm = 500 + 100s, where s = 14 years (average years of schooling for men)
wm = 500 + 100(14) = 1900
wf = 300 + 75s, where s = 12 years (average years of schooling for women)
wf = 300 + 75(12) = 1200
Step 2: Calculate the explained component of the wage differential by estimating the wage differential that can be explained by the differences in observable characteristics (years of schooling) between the two groups.
Explained wage differential = [500 + 100(14)] - [300 + 75(12)] = 700
Step 3: Calculate the unexplained component of the wage differential, which is the portion that cannot be explained by observable characteristics and may be attributed to discrimination or unobserved factors.
Unexplained wage differential = Actual wage differential - Explained wage differential
Unexplained wage differential = 700 - 700 = 0
In this case, the unexplained component of the wage differential is zero, indicating that none of the wage differential can be attributed to discrimination. All of the wage differential can be explained by the differences in observable characteristics (years of schooling) between male and female workers.
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Which expression is equivalent to 12.8-3s+15.5+8s?
A. -2+5s
B. 5s +28.3
C. 33.3s
D. 27.3 +5s
Answers
The correct expression which is equivalent to 12.8 - 3s + 15.5 + 8s is,
⇒ 5s + 28.3
We have to given that;
Expression to solve is,
⇒ 12.8 - 3s + 15.5 + 8s
Now, WE can simplify as;
⇒ 12.8 - 3s + 15.5 + 8s
Combine like terms,
⇒ 12.8 + 15.5 - 3s + 8s
⇒ 28.3 + 5s
⇒ 5s + 28.3
Thus, The correct expression is,
⇒ 5s + 28.3
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resolve into factors:- 1+b²+b⁴
Answers
1+b²+b⁴ can be resolved into factors (1+b²+b),(1+b²- b).
We will evaluate 1+b²+b⁴ with the help of algebraic identities,
We can write 1+b²+b⁴ as,
1+b²+b⁴ = 1+(b)²+(b²)²
= 1+(b)²+(b)²+(b²)²-b² (Adding and subtracting b²)
= 1+2(b²)+(b²)²-(b)²
= (1)²+2(b²)(1)+(b²)²- (b)²
Now using the identity (a + b)²= a²+b²+2ab, we have,
1+b²+b⁴ = (1+b²)²- (b)²
= (1+b²+b)(1+b²- b) [By using identity a²-b²= (a+b)(a-b)]
Therefore, the correct answer is 1+b²+b⁴= (1+b²+b)(1+b²- b).
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Ms Brown's left at 9:00 a. M. Her plane landed 1 hour and 23minute later. What time her plane land
Answers
Answer:
10:23 am
Step-by-step explanation:
We Know
Ms. Brown left at 9:00 am
Her plane landed 1 hour and 23 minutes later.
What time does her plane land?
We Take
9:00 + 1:23 = 10:23 am
So, her plane landed at 10:23 am
Which graph shows the line of best fit for the data ?
Answers
Answer:
Bottom left
Step-by-step explanation:
It covers the most points
What is the displacement of the particle in the time interval 7 seconds to 8 seconds?
A. 0 meters
B. 1.5 meters
C. 3 meters
D. 7 meters
Answers
The correct option is B, the displacement is 1.5 meters.
How to find the displacement?Displacement is defined as the difference between the final position and the initial position.
Here we can see a graph that gives the velocity as a function of time.
The velocity at t = 7s is 0m/s
The velocity at t = 8s is 3m/s
Then the acceleration in that interval is:
A = (3m/s - 0m/s)/(8s - 7s) = 3m/s²
And the position will be:
P = (1/2)*3m/s²*(t - 7s)²
Now take the differenve between the positions at t = 8s and t = 7s, we will get:
displacement = (1/2)*3m/s²*(8s - 7s)² - (1/2)*3m/s²*(7s - 7s)² = 1.5m
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Find the value of x.
Answers
Answer:
x = 46
Step-by-step explanation:
These 2 angles would add up to 180 degrees.
So 41 + (3x+1) = 180
Let's solve for x.
41 + 3x + 1 = 180
Combine like terms.
42 + 3x = 180
subtract 42 from both sides
3x = 180-42
3x = 138
divide both sides by 3
x = 46
find the length of or−→−. r=(2,8,6)
Answers
Answer:
2sqrt(26)
Step-by-step explanation:
sqrt(2^2+ 8^2+ 6^2)
=2×sqrt(26)
Can you pls explain how you got the answer?
Answers
Answer:
1. D.
2. b
Step-by-step explanation:
1.Change to 2.375 to a fraction
2.735=19/8
2. 6^2=36
8^2=64
36+64=10^2
36+64=100
100=100
Question 2:
Choose D.
[tex]\frac{19}{8} = 2\frac{3}{8} =2.375[/tex]
Look at the fraction 19/8.
The numerator (19) is greater than the denominator (8). That means we have a number > 1.
So how many 8's are in 19?
Well, 8 x 2 = 16. So that would be 16/8 = 2.
Then we'd have 3 leftover because 19-16 = 3.
That's how we know that 19/8 = 2 3/8.
Are you allowed to use a calculator? Because if so, 3/8 = 0.375. That's the fastest way to figure it out!
If not, we can do it the old fashioned way (ha). 3/8 is halfway between 2/8 and 4/8.
2/8 = 1/4 = 0.25 (1/4 = one quarter, just like a quarter worth 0.25)
4/8 = 1/2 = 0.50 (1/2 = a half, a half dollar, 0.50)
0.25 + 0.50 = 0.75 >>> Now divide that by 2 to find the halfway between 0.25 and 0.50 = 0.75/2 = 0.375.
^^^^ That's just a workaround way of figuring out 3/8 as a decimal if you can't use a calculator.
Question 3: Use the pythagorean theorem. a^2 + b^2 = c^2.
C is the hypotenuse, aka the LONGEST length of the right triangle.
If the numbers work in that formula, it's a right triangle. If not, it's NOT a right triangle.
Marissa: 5, 12, 13
Does 5^2 + 12^2 = 13^2?
25 + 144 = 169
13^2 = 169
So YES, Marissa can make a right triangle.
Berta: 6, 8, 10
6^2 + 8^2 = 100 = 10^2
So YES, Berta can make a right triangle.
Corrin: 12, 16, 20
12^2 + 16^2 = 400 = 20^2
So YES, Corrin can make a right triangle.
So the answer is D, all 3 can make right triangles.
Find a Cartesian equation for the curve and identify it.r = 4sin(θ) + 4cos(θ)
Answers
To convert the polar equation r = 4sin(θ) + 4cos(θ) into a Cartesian equation, we can use the identities:
x = r cos(θ)
y = r sin(θ)
Substituting r = 4sin(θ) + 4cos(θ) into these identities, we get:
x = (4sin(θ) + 4cos(θ))cos(θ) = 4sin(θ)cos(θ) + 4cos²(θ)
y = (4sin(θ) + 4cos(θ))sin(θ) = 4sin²(θ) + 4sin(θ)cos(θ)
Simplifying these expressions using the trigonometric identity sin²(θ) + cos²(θ) = 1, we obtain:
x = 4cos(θ) + 4cos²(θ)
y = 4sin(θ) + 4sin(θ)cos(θ) = 4sin(θ) + 4cos(θ)sin(θ)
Therefore, the Cartesian equation for the curve is:
(x - 4)² + y² = 16
This equation represents a circle with center (4, 0) and radius 4. The original polar equation r = 4sin(θ) + 4cos(θ) can be interpreted as the distance from the origin to a point on the circle, measured along a line that makes an angle of θ with the positive x-axis.
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triangle BCD is dilated by a scale factor 3/4 to form triangle B’C’D’. side CD measures 10. what is the measure of side C’D’?
Answers
Answer:
Step-by-step explanation:If triangle BCD is dilated by a scale factor of 3/4 to form triangle B’C’D’, and side CD measures 10, then the measure of side C’D’ would be 7.5.
Which group of voters has the greatest percentage of student voters?
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has one hundred twenty and two hundred forty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has one hundred fifty and two hundred fifty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has two hundred and four hundred fifty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has three hundred fifty and nine hundred.
11 of 20 Questions
Answers
For the first table:
Student Voters: 120
Total Voters: 240
Percentage of student voters: (120 / 240) * 100 = 50%
For the second table:
Student Voters: 150
Total Voters: 250
Percentage of student voters: (150 / 250) * 100 = 60%
For the third table:
Student Voters: 200
Total Voters: 450
Percentage of student voters: (200 / 450) * 100 = 44.44...%
For the fourth table:
Student Voters: 350
Total Voters: 900
Percentage of student voters: (350 / 900) * 100 = 38.88...%
Based on these calculations, the second table, with a percentage of 60% student voters, has the greatest percentage of student voters.
If nominal wages and prices are not flexible which of the following must be true when the economy has a severe recessionary gap? (A The aggregate demand curve is vertical (B The aggregate demand curve is horizontal (CThe short run aggregate supply curve is vertical DThe short run aggregate supply curve is upward sloping (E) The short run aggregate supply curve is hotizontal
Answers
If nominal wages and prices are not flexible, then the short-run aggregate supply curve is vertical.
This means that the economy is operating at full employment, and any increase in aggregate demand will not result in an increase in output but rather lead to higher prices.
In other words, the economy is supply-constrained, and there is no excess capacity to produce more output in response to an increase in demand.
In a severe recessionary gap, the economy is operating below its potential output, and there is excess capacity in the economy. However, if nominal wages and prices are not flexible, firms cannot adjust their prices downwards,
and wages cannot be reduced, leading to a situation where the short-run aggregate supply curve is vertical.
This results in a situation where any increase in aggregate demand will not lead to an increase in output, and the economy remains stuck in a recessionary gap with high unemployment and low output.
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please i need help on this
Answers
Answer:
b
Step-by-step explanation:
Let FR,A, FR,B, FR,C, FR,D, FR,E, and FR,F be the magnitudes of the equivalent resultant loads for each of the six cases. Rank the magnitudes of the resultant forces for the six cases. Rank the items from smallest to largest. To rank items as equivalent, overlap them. Let FR,A, FR,B, FR,C, FR,D, FR,E, and FR,F be the magnitudes of the equivalent resultant loads for each of the six cases. Rank the magnitudes of the resultant forces for the six cases. Rank the items from smallest to largest. To rank items as equivalent, overlap them. As well When measuring from the left side of the beam, x¯A, x¯B, x¯C, x¯D, x¯E, and x¯F are the locations where the resultant force is applied in each of the six cases. Rank these six locations. Rank the items from smallest to largest. To rank items as equivalent, overlap them
Answers
The magnitudes of the resultant forces and the locations where the resultant force is applied can be ranked from smallest to largest as described above. It is important to note that when there are equivalent values, they should be ranked as such and overlap.
To rank the magnitudes of the resultant forces for the six cases, we first need to determine the equivalent resultant load for each case. The equivalent resultant load is the single force that has the same effect on the beam as the distributed load or loads in the original problem.
The magnitudes of the equivalent resultant loads for each case are:
FR,A < FR,C = FR,D < FR,E < FR,B < FR,F
Therefore, we can rank the magnitudes of the resultant forces as follows, from smallest to largest:
FR,A < FR,C = FR,D < FR,E < FR,B < FR,F
When measuring from the left side of the beam, x¯A, x¯B, x¯C, x¯D, x¯E, and x¯F are the locations where the resultant force is applied in each of the six cases.
The locations where the resultant force is applied are:
x¯C < x¯D < x¯B < x¯E < x¯A < x¯F
Therefore, we can rank the locations where the resultant force is applied as follows, from smallest to largest:
x¯C < x¯D < x¯B < x¯E < x¯A < x¯F
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Mr. Wilson is packing orders for his soap business. One customer ordered 12 bars of his Minty Morning soap. If each bar of soap weighs 120 grams, how many kilograms will this order weigh?
Answers
Answer:
1.440kg
Step-by-step explanation:
12 × 120=1440g
converting g to kg, divide by 1000 as 1000g = 1kg
Answer is therefore given as 1.440kg
What is the slope from (−7, 5) to (−3, 4)?
Answers
Answer:
m = -1/4
Step-by-step explanation:
Slope = rise/run (y2 - y1) / (x2 - x1)
Points (−7, 5) (−3, 4)
We see the y decrease by 1, and the x increase 4, so the slope is
m = -1/4
The radius of Circle A is 8 cm. The radius of Circle B is 2 cm greater than the radius of Circle A. The radius of Circle C is 4 cm greater than the radius of Circle B. The radius of
Circle D is 3 cm less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
Answers
The area of Circle B is 301.59 cm² (rounded to two decimal places).
The area of Circle C is 452.39 cm² (rounded to two decimal places).
The area of Circle D is 407.15 cm² (rounded to two decimal places).
The area of Circle D is 2.03 times greater than the area of Circle A (rounded to two decimal places).
The radius of Circle C is 10 + 4 = 14 cm.
The radius of Circle D is 14 - 3 = 11 cm.
The area of Circle A is π(8)^2 = 64π square cm.
The area of Circle B is π(10)^2 = 100π square cm.
The area of Circle C is π(14)^2 = 196π square cm.
The area of Circle D is π(11)^2 = 121π square cm.
The area of Circle D is 121π/64π = 1.89 times greater than the area of Circle A.
A small sofa has a mass of 6 kilograms. A pillow on the sofa has a mass of 100 grams. How many pillows would it take to equal the mass of the sofa?
Answers
Answer:
6000
Step-by-step explanation:
solved
what is the probability that at least 30 of the women in the sample will not meet the age requirement
Answers
To calculate the probability that at least 30 of the women in the sample will not meet the age requirement, we need to use the binomial distribution formula:
P(X >= 30) = 1 - P(X < 30)
where X is the number of women who do not meet the age requirement, and P(X < 30) is the cumulative probability of X being less than 30.
The probability of a woman not meeting the age requirement is given as 0.2, so the probability of a woman meeting the age requirement is 0.8. We are sampling 200 women, so the number of women who do not meet the age requirement follows a binomial distribution with n = 200 and p = 0.2.
Using a binomial calculator or software, we can find that P(X < 30) = 0.1656. Therefore, the probability of at least 30 women not meeting the age requirement is:
P(X >= 30) = 1 - P(X < 30) = 1 - 0.1656 = 0.8344
Therefore, the probability that at least 30 of the women in the sample will not meet the age requirement is 0.8344, or approximately 83.44%.
Learn more about probability here:
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You are solving x²-3x-10=0 using the quadratic formula Simplify the radical numerator and denominator
Answers
Answer:
Step-by-step explanation:To solve the quadratic equation x² - 3x - 10 = 0 using the quadratic formula, we first identify the values of a, b, and c:
a = 1
b = -3
c = -10
Now, we can apply the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we have:
x = (-(-3) ± √((-3)² - 4(1)(-10))) / (2(1))
Simplifying further:
x = (3 ± √(9 + 40)) / 2
x = (3 ± √49) / 2
x = (3 ± 7) / 2
This gives us two possible solutions:
x₁ = (3 + 7) / 2 = 10 / 2 = 5
x₂ = (3 - 7) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation x² - 3x - 10 = 0 are x = 5 and x = -2.