Answer:
14.04°
Step-by-step explanation:
In this right triangle, we're seeking the measurement of an angle at the base of the triangle and we have the measurements of two of the sides (none are the hypotenuse) : the opposite one of the angle and the adjacent side.
The relationship between the two sides we have the measurement and the angle we are looking for is the tangent:
[tex]tan(\alpha) = \frac{a}{b} = \frac{5}{20} = 0.25[/tex]
To find the angle we do an arctan on 0.25 and we get an angle of 14.04 degrees.
Answer:
14.04
Step-by-step explanation:
i took the test
Identify the circumference of ⊙S in which A=64π ft^2. HELP ASAP!!
C = 24π ft
C = 32π ft
C = 16π ft
C = 8π ft
Answer:
C = 16π ft
Step-by-step explanation:
If we know the area
A = pi r^2
64 pi = pi r^2
Divide each side by pi
64 = r^2
Take the square root of each side
8 = r
The radius is 8
Now we can find the circumference
C = 2 *pi*r
C = 2*pi*8
C = 16pi
Answer:
[tex]\large\boxed{C=16\pi\ ft^2}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A_O=\pi r^2[/tex]
r - radius
We have
[tex]A_O=64\pi\ ft^2[/tex]
Substitute:
[tex]\pi r^2=64\pi[/tex] divide both sides by π
[tex]r^2=64\to r=\sqrt{64}\\\\r=8\ ft[/tex]
The formula of a circumference:
[tex]C=2\pi r[/tex]
Substitute:
[tex]C=2\pi(8)=16\pi\ ft[/tex]
A census determines the number of people living in the United States. Identify the type of data.
A.
categorical data
B.
quantitative data
C.
continuous data
D.
attribute data
Answer with explanation:
Census Evaluates number of people Living in the United States.
There are two kinds of Data
1. Qualitiative----Which Says about the Quality Possessed by variate in Data set.
2. Quantitative----Variate in Data set is represented through numerical value.
Quantitative Data set has two attributes
(a) Discrete Data Set
(b) Continuous Data set
In this Question , it has been asked about number of people living in United states , which is Numerical Representation.As when number of People will get counted , it will keep on increasing, but population measurement which is represented by Natural number can't be continuous.
So, it is Quantitative data.
Option (B)--- Quantitative data.
1. The fabric Josef is using comes in 100 square-inch pieces that cost $6.25 each. What will his fabric cost? Show your work.
2. a student made a toy chest for his baby sister's square building blocks. Six layers of blocks can fit in the box, and each layer has 15 blocks. How many building blocks can the toy chest hold? show your work.
PLEASE HELP
Answer:
The asnwers for your two question problem are
1. $625
2. 90 building blocks
Step-by-step explanation:
First problem
The fabric Josef is using comes in 100 square-inch pieces that cost $6.25 each. What will his fabric cost?
* The fabric has 100 pieces
* Each piece costs $6.25
Total amount for the fabric = $6.25*100 = $625
Second problem
A student made a toy chest for his baby sister's square building blocks. Six layers of blocks can fit in the box, and each layer has 15 blocks. How many building blocks can the toy chest hold?
* 6 layers of blocks fit in the box
* Each layer has 15 blocks
Total amount of blocks = 6*15 blocks = 90 blocks
etermine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 3 2 x − 2y = 4 x + 1 3 y = 2 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answer:
(32/15, -2/5)
Step-by-step explanation:
(1) ³/₂x - 2y = 4
(2) x + ⅓y = 2
(3) 3x - 4y = 8 Multiplied (1) by 2
(4) 3x + y = 6 Multiplied (2) by 3
5y = -2 Subtracted (3) from (4)
(5) y = -⅖ Divided each side by 5
x + ⅓(-⅖) = 2 Substituted (5) into (2)
x - ²/₁₅ = 2
x = 2 + ²/₁₅ Added ²/₁₅ to each side
x = 32/15
The system of equations has only one solution: (32/15, -2/5).
Drag the numbers to order them from greatest to least, with the greatest at the top.
9.92749.....
√101
0.99853.......
10√
Howdy!
I just finished taking the quiz and found that the correct answer is:
10[tex]\pi[/tex]
√101
9.92749...
0.99853...
I hope this helped! :D
The numbers, from greatest to least, are 9.92749....., √101 (approximately 10.0499), 10√ (approximately 3.1623), and 0.99853....... The principles of significant digits are important in ordering these numbers to ensure accuracy without introducing errors by rounding.
Explanation:First, we need to evaluate the values given to us:
9.92749..... (This is a repeating decimal, so it retains its value as 9.92749...)√101 (This is the square root of 101, which is approximately 10.0499.)0.99853....... (This is another repeating decimal, and it remains as 0.99853...)10√ (This likely means the square root of 10, which is approximately 3.1623.)Now we will order them from greatest to least:
9.92749.....√101 (Approximately 10.0499)10√ (Approximately 3.1623)0.99853.......We keep in mind the principles of significant digits when we compare or order these numbers.
As evident from the provided reference information, it is important not to introduce errors by unnecessary rounding.
Select the first correct reason why the given series converges.
a. convergent geometric series
b. convergent p-series
c. integral test
d. comparison with a convergent p-series
e. converges by limit comparison test f. converges by alternating series test e 1. ∑n=2∞n2+n‾√n4−4 f 2. ∑n=1∞n2+ln(n)n2−9n f 3. ∑n=1∞(cos(nπ))ln(6n) f 4. ∑n=1∞(−1)n7n+5 f 5. ∑n=1∞(−1)nn‾√n+4 c 6. ∑n=2∞4n(ln(n))2
Answer:
E. Converges by limit comparison test.
Step-by-step explanation:
Here is something that might help you on this
https://study.com/academy/answer/select-the-first-correct-reason-why-the-given-series-converges-displaystyle-sum-n-1-infty-1-n-frac-sqrt-n-n-2-a-convergent-geometric-series-b-convergent-p-series-c-comparison-or-limi.html.
This question involves the application of different series convergence tests in calculus. The first correct reasons why the given series converged were identified using the comparison to a convergent p-series, integral test, and the alternating series test.
Explanation:This question relates to the convergence of series in calculus. In order to determine why a given series converges, we need to apply various convergence tests. Here are the first correct reasons why the provided series converge:
∑n=2∞n2+n/√n4−4 converges by comparison with a convergent p-series.∑n=1∞n2+ln(n)/n2−9n converges by the integral test.∑n=1∞(cos(nπ))ln(6n) converges by the alternating series test.∑n=1∞(−1)n/7n+5 converges by the alternating series test.∑n=1∞(−1)n/√n+4 converges by the alternating series test.∑n=2∞4n(ln(n))2 converges by the integral test.Learn more about Convergence of Series here:https://brainly.com/question/33953891
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Given that tan theta = square root of 3 over 4, and 0 < theta < pi over 2, what is the exact value of cot theta?
Answer:
[tex]\frac{4\sqrt{3} }{3}[/tex]
Step-by-step explanation:
4sqrt3/3
The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,500 per day. FSF supplies hot dogs to local restaurants at a steady rate of 260 per day. The cost to prepare the equipment for producing hot dogs is $66. Annual holding costs are 46 cents per hot dog. The factory operates 296 days a year. a. Find the optimal run size. (Do not round intermediate calculations. Round your answer to the nearest whole number.) Optimal run size b. Find the number of runs per year. (Round your answer to the nearest whole number.) Number of runs c. Find the length (in days) of a run. (Round your answer to the nearest whole number.) Run length (in days)
Answer:
a. 5218 hot dogs
b. 18 runs per year
c. 1 day per run
Step-by-step explanation:
(a) Let n represent the number of hotdogs in an optimal run. The number of runs needed in a year is ...
r = (260 hotdogs/day)·(365 days/year)/(n hotdogs/run) = 94900/n runs/year
The number of hotdogs in storage decreases from n at the end of a run to 0 just before a run. The decrease is linear, so the average number in storage is n/2.
We can go to the trouble to write the equation for total cost, then differentiate it to find the value of n at the minimum, or we can just jump to the solution. That solution is ...
holding cost = setup cost
(n/2)·0.46 = (94900/n)·66
n^2 = 94900·66·2/0.46 = 27,232,173.9
n ≈ 5218.446
The optimal number of hotdogs in a run is 5218.
___
(b) The number of runs needed per year is (from part (a)) ...
r = 94900/5218 ≈ 18.187
The number of runs per year is 18.
___
(c) The run lenght is 5218 hotdogs, and the run produces them at the rate of 5500 hotdogs/day, so the run length in days is ...
(5218 hotdogs)/(5500 hotdogs/day) = 0.9487 days
The run length is 1 day.
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 13 subjects had a mean wake time of 102.0 min. After treatment, the 13 subjects had a mean wake time of 79.4 min and a standard deviation of 21.2 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 90% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 102.0 min before the treatment? Does the drug appear to be effective?
Answer:
Confidence interval: 11.5 < µ < 30.9
Read below to see conclusion:
Step-by-step explanation:
n = 13, x = 79.4, s = 21.2, Z = 1.645 (z score for a confidence interval with 90% confidence)
Use the formula to find the error: E = Z(s/√n)
We have: E = 1.645(21.2/√13) = 9.7
Now construct the confidence interval:
x - E < µ < x + E
21.2 - 9.7 < µ < 21.2 + 9.7
11.5 < µ < 30.9
Yes, the drug appears to be effective because the estimated wake time for a population using this drug will be between 11.5 and 30.9 minutes. The upper end of this interval is much lower than 102, so it appears as though the drug is effective.
4O POINTS AND BRAINLIEST!!!!!!!!!!!!
1. The value of y varies directly with x, and y = 12 when x = −6.
Find y when x = −4.
2. The value of y varies directly with x, and y = 3 when x = −6.
Find y when x = 1.
3. The value of y varies directly with x, and y = −12 when x = 6.
Find y when x = −4.
4. The value of y varies directly with x, and y = 3 when x = 1.
Find y when x = −5.
1. 8 (k=-2)
2. 8 (k=-0.5)
3. 8 (k=-2)
4. -15 (k=3)
A field is to be fertilized at a cost of $0.07 per square yard. The rectangular part of the field is 125 yards long and the diameter of each semicircle is 40 yards. Find the cost of fertilizing the field. Use 3.14 for π.
Answer:
Total cost is $437.92
Step-by-step explanation:
Rectangular area=125•40=5000 yd²
Two equal semicircles=one single circle
Area of circle=πr²=20²•π=400•3.14=1256 yd²
Total field area=circle+rectangle=6256yd²
Cost=area•0.07yd²=6256•0.07=437.92
Thad is riding his bike to the library,which is 3 kilometers away. How many meters away is the library?
Answer: The library is 3,000 meters away.
Step-by-step explanation:
The solution of this exercise can be obtained by making the conversion from kilometers to meters.
You know that the library is 3 kilometers away.
Let's remember that 1 kilometer has 1,000 meters.
Then, the conversion from 3 kilometers to meters can be made by this proccedure:
3 kilometers to meters:
[tex]=(3\ kilometers)(\frac{1,000\ meters}{1\ kilometers})\\\\=3,000\ meters[/tex]
Then the library is 3,000 meters away.
Write the ratio as a fraction in simplest form. The ratio for 18 girls to 27 boys as a fraction is .
Answer:
2/3
Step-by-step explanation:
Reduce the fraction 18/27 into its lowest terms
since both 18 and 27 are divisible by 9, divide both terms by 9
18/9 = 2
27/9 = 3
18/27 reduced to lowest terms is 2/3
Is the sum of two rational number is 5/18 if one of the number is 1/8 find the other
Answer: 4/8
Step-by-step explanation:
Equation: 1/8+x=5/18
-1/8 -1/8
x=4/8
Double Check: 4/8+1/8=5/8
According to Cavaliert's Principle, which two triangles have the same area?
According to Cavaliert's Principle,
if two triangles are formed on base of equal length and are between same parallels, i.e have same height, then the triangles are of equal area.
Identify the graph of 4x^2+5y^2=20 for T(5,-6) and write an equation of the translated or rotated graph in general form..
Answer:
The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0 ⇒ answer (b)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* 4x² + 5y² = 20
∵ A = 4 , B = 0 , C = 5
∴ B² - 4 AC = (0)² - 4(4)(5) = -80
∴ B² - 4AC < 0
∴ The graph is ellipse or circle
* If A and C are nonzero, have the same sign, and are not
equal to each other, then the graph is an ellipse.
* If A and C are equal and nonzero and have the same
sign, then the graph is a circle.
∵ A and C have same signs with different values
∴ It is an ellipse
* Now lets study T(5 , -6), that means the graph will translate
5 units to the right and 6 units down
∴ x will be (x - 5) and y will be (y - -6) = (y + 6)
* Lets substitute the x by ( x - 5) and y by (y + 6) in the equation
∴ 4(x - 5)² + 5(y + 6)² = 20
* Use the foil method
∴ 4(x² - 10x + 25) + 5(y² + 12y + 36) = 20
* Open the brackets
∴ 4x² - 40x + 100 + 5y² + 60y + 180 = 20
* Collect the like terms
∴ 4x² + 5y² - 40x + 60y + 280 = 20
∴ 4x² + 5y² - 40x + 60y + 280 - 20 = 0
∴ 4x² + 5y² - 40x + 60y + 260 = 0
* The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0
Answer:
BBBBBB
Step-by-step explanation:
BBBBB
(2Q) The graph of the logarithmic function y = loga(x) always passes through what point?
Answer:
(1,0)
Step-by-step explanation:
The given logarithmic function is
[tex]y=\log_ax[/tex]
When [tex]x=1[/tex], the logarithmic function becomes;
[tex]y=\log_a1[/tex]
[tex]\Rightarrow y=\log_aa^0[/tex]
[tex]\Rightarrow y=0(\log_aa)[/tex]
[tex]\Rightarrow y=0(1)[/tex]
[tex]\Rightarrow y=0[/tex]
Therefore the graph always passes through;
[tex](1,0)[/tex]
Answer:
option D
(1,0)
Step-by-step explanation:
Given in the question an expression
y = [tex]log_{a}x[/tex]
This function's graph will always pass through x-axis where y will always be 0
y = [tex]log_{a}x[/tex]
0 = [tex]log_{a}x[/tex]
This situation is only possible when x = 1
0 = [tex]log_{a}1[/tex]
Secondly, x can never be zero
As,
[tex]y = log_{a}0[/tex] is undefined
so this eliminate option (A) and (C)
Use the graph to determine the functions type of zeros.
The quadratic function has zeros at x = -2, x = 0 (with multiplicity 2), x = 2, and x = 6. The zeros include simple roots and a double root, determined by the graph's behavior at the x-intercepts.
To determine the type of zeros for a quadratic function based on its graph, we need to consider the behavior of the parabola at the x-intercepts (zeros). The given points where the graph intersects the x-axis are (-2, 0), (0, 0), (2, 0), and (6, 0).
1. **Multiplicity of Zeros:**
- For the point (0, 0), the zero has multiplicity 2 since the graph touches the x-axis but doesn't cross it.
- For the points (-2, 0), (2, 0), and (6, 0), the zeros have multiplicity 1 since the graph crosses the x-axis at these points.
2. **Type of Zeros:**
- For the zero at x = 0 (multiplicity 2), it is a double root or a repeated zero.
- For the zeros at x = -2, x = 2, and x = 6 (multiplicity 1), they are simple roots.
3. **Discriminant:**
- The discriminant of a quadratic equation \(ax^2 + bx + c = 0\) is given by \(b^2 - 4ac\).
- If the discriminant is positive, the quadratic equation has two distinct real roots (simple roots).
- If the discriminant is zero, the quadratic equation has one real root with multiplicity 2 (double root).
- If the discriminant is negative, the quadratic equation has two complex conjugate roots.
In this case, the fact that the parabola touches the x-axis at (0, 0) without crossing it indicates a double root at x = 0. The other zeros at (-2, 0), (2, 0), and (6, 0) are simple roots.
Therefore, the type of zeros for the given quadratic function is a mix of simple roots and a double root.
Learn more about type of zeros here:
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What is the value of x?
The little rectangle in the top right means the angle is a right angle which equals 90 degrees.
This also means all the other angles are also 90 degrees.
Solve for x:
2x+8 = 90
Subtract 8 from both sides:
2x = 82
Divide both sides by 2:
x = 82/2
x = 41
Answer:
x = 41
Step-by-step explanation:
Since they are vertical angles, 90 = 2x + 8.
Then isolate the variable by subtracting 8 from both sides.
So 2x = 82.
Then divide each side by 2 to get x = 41.
Which values of x would make a polynomial equal to zero if the factors of the polynomial wrre (x+6) and (x+9)?
Negative 6 and negative 9 would :)
Polynomials are mathematical expressions involving variables raised with non-negative integers, coefficients and constants. The value of the solution that will make the polynomial equal to zero is -6 and -9.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
The values of x that would make a polynomial equal to zero if the factors of the polynomial are (x+6) and (x+9) are -6 and -9.
Learn more about Polynomials:
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If the Jonas family wanted to plant 3 bushes that needed to be 3 feet apart and 3 feet away from the fence around the yard, would they have room?
Answer:
Not enough info.
Step-by-step explanation:
Not enough information, how big is the fence perimeter wise? What is the shape of the fence? If the fence is square and 2,000 feet long, of course there's room. If its a square fence that's 2 feet long, there is no room at all.
Can you help me with this question? Complete the proof and show your work.
4. ∠FCB ≅ ∠GDC: Corresponding angles theorem (when two parallel lines are crossed by a transversal, the corresponding angles formed are congruent) (but to use this, you have to state that ∠BCF and ∠CDG are corresponding)
5. ∠FCB ≅ ∠GCD: Subst. POC (Because ∠FCB ≅∠GDC and ∠GDC≅∠GCD)
6. Converse of the corresponding angles theorem
I can not really show my work since most proofs are theoretical and hence most work is done in the head.
Andrea bought tacos from a food truck and left a 25% percent tip of $2.00. What was the price of Andrea's tacos before tip
$8.00. Hope this helps!
help please thank you
Answer:
Step-by-step explanation:
The first two are incorrect. Only very special n's will work. (Every 10th one for n>0)
Just call A and B incorrect.
400o = 360 + 40
The answer is between C and D
The question is will a negative value for n work? Suppose n = - 1 That means you go around the circle clockwise 1 time and though the question does not say it, you must start at the positive x axis.
Having said that 40 is plus.
The 360 starts at the + x axis. It doesn't matter how it got there. 40 degrees from the +x axis is in the first quadrant. It always will be.
D is correct but C is the better answer because it includes D.
25 POINTS ANS BRAINLIEST
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Based on visual inspection of the dot plots, which group appears to have the longest average forearm length?
Group A, because seven children have a forearm length longer than 10 inches
Group B, because two children have a forearm length longer than 10 inches
Group A, because one child in the group has the least forearm length of 9 inches
Group B, because three children in the group have the least forearm length of 9 inches
Answer: it is a
Step-by-step explanation:
It is a because if you add them all together you will see that be is less so you can cross does out so you are left with a or c. C is not the correct ans because none of the kids had a forearm less than 9. And all seven of the kids had a forearm more than 10 inches.
This is literally 20 points of my grade pls help! very desperate.
Answer:
Step-by-step explanation:
see attached
A town uses positive numbers to track increases in population and negative numbers to track decreases in population. The population has decreased by 300300300 residents over the past 555 years. The same number of residents left each year. What was the change in the town's population each year?
Answer:
-60 people
Step-by-step explanation:
The change in population was -300 people.
The change in population was -300 people/5 yr or -60 people/yr.
A 20-foot support post leans against a wall, making a 70° angle with the ground. to the nearest tenth of a foot, how far up the wall will the support post reach
Trigonometry
[tex]Sin\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite}[/tex]
[tex]S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]
You know the hypotenuse and you want to find the opposite therefore you use, sine.
[tex]Opposite = Sin(70) *{20}[/tex]
Opposite = 18.79385242
Opposite = 18.8 feetWhat is the period for the tangent function? (Answer in radians and round to the hundreds place.)
Answer: _____
Answer:
π radians.
3.14.
Step-by-step explanation:
The period is π radians which is 3.14 radians to the nearest hundredth.
Assume the random variable X is normally distributed with mean mu equals 50?=50 and standard deviation sigma equals 7?=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35) LOADING... Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35)?? A. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve between the vertical line segments is shaded. B. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the right of the left vertical line segment is shaded. C. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the left of the left vertical line segment is shaded. Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35)equals=nothing ?(Round to four decimal places as? needed.)
Answer:
B. A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the right of the left vertical line segment is shaded; P(X > 35) = 0.9838
Step-by-step explanation:
The middle line in a normal distribution represents the mean. The mean of this distribution is 50; this means the peak of the curve will have a vertical line down to the horizontal axis at 50.
The value we are concerned with is anything more than 35. This means there will be a vertical line from the horizontal axis to the curve at 35. Since we want the probability X is greater than 35, the area to the right of this value under the curve will be shaded.
To find the probability, we use a z score. The formula for z scores is
[tex]x=\frac{X-\mu}{\sigma}[/tex]
Using our values for X, the mean and the standard deviation, we have
[tex]z=\frac{35-50}{7}=\frac{-15}{7}=-2.14[/tex]
Using a z table, we see that the area under the curve to the right of this value is 0.0162. This means the area to the left, the desired area, is
1-0.0162 = 0.9838.