Answer:
x ≈ 38.61
Step-by-step explanation:
using the tangent ratio in the right triangle
tan47° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{35}\) ( multiply both sides by 35 )
35 × tan47° = x , then
x ≈ 37.53 ( to 2 dec. places )
Factor this equation please
Answer:
the answer is ç (3x+4)(x+7)
Find the midpoint of the segment between the points (−5,13) and (6,4)
Answer:
(0.5, 8.5)
Step-by-step explanation:
use this formula ((x1+x2/2), (y1+y2/2)) if you use desmos graphing calculator and you type this formula in, all you have to do it put in the correct numbers and you get your midpoint.
Hope this helped :)
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
We have given that, the points (−5,13) and (6,4)
We have to determine the midpoints
What is the formula for the midpoint?((x1+x2/2), (y1+y2/2))
x1=-5,x2=6,y1=13 and y2=4
-5+6/2=1/2=0.5
and next is,
13+4/2=17/2=8.5
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
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Translate this phrase into an algebraic expression, Nine more than the quotient of a number and 7 is 6
Answer:
x/7 + 9 = 6
Step-by-step explanation:
Hope this helps! Please give brainliest!
(6w — 11w^2)-(4+7w^2)
Answer:
-18w^2 + 6w - 4
Explanation:
Given the expression (6w — 11w^2)-(4+7w^2)
Open the bracket
6w — 11w^2 - 4 - 7w^2
= -11w^2-7w^2 + 6w -4
= -18w^2 + 6w - 4
Hence the required expansion is -18w^2 + 6w - 4
Choose all the expressions that equal 36.
Responses
A (14⋅32)2−28open paren 1 fourth times 32 close paren squared minus 28
B 23 + (58−54)2 + 122 3 + ( 58 - 54 ) 2 + 12
C 92 − (43 + 32) + 3005092 − ( 4 3 + 3 2 ) + 300 50
D 124 + (82 − 42) − 99124 + ( 8 2 − 4 2 ) − 99
E 53 − (2. 5 × 30) − 20
The expressions that equal 36 is:
E) 53 − (2. 5 × 30) − 20
Calculation of Algebra ExpressionEvaluated the mathematical expressions in each response to see if they equal 36.
A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.
B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.
C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.
D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.
Thus, only the expressions listed in my previous answer equal 36.
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ken makes 75 cookies. He gives 3/5 of them to his classmates and 1/3 of them to his teachers. He brings the rest home. Ken brings home _______ cookies.
Answer:
5 cookies
Step-by-step explanation:
3/5 = 9/15 1/3=5/15
5/15+9/15=14/15.
75 ÷ 15 = 5
Ken will bring home 5 cookies
Craig likes to collect vinyl records but decided to sell a few. Last year he had 120 records in his collection. Now he has 100 records. What is the percent change and is it an increase or a decrease?
Salut/Hello!
Answer: 16,(6)% and it's a decrease
Step-by-step explanation:
/ - fraction line
initial records = 120
after selling = 100
=> records sold = 120 - 100 = 20
We know that:
100% = 120/100 => 1% = 1.2/100
120 - 100 = 20
So we can find: 20 : 1.2 = 16,(6)%
Because 5% = 6 and 6 : 1.2 = 5%
So by knowing the amount of records sold and the percentage per record we divide them and find out the percentage of records sold.
I hope it'll be useful! :]
Use the following image to complete the sentences describing the ratio of spots to eyes.
A ladybug with 2 eyes and 6 spots.
A ladybug with 2 eyes and 6 spots.
There are 6 spots for every
eyes.
There are
spots for every 1 eye.
Using ratios, the sentences are completes as follows:
There are 6 spots for every 2 eyes.There are 3 spots for every 1 eye.What is the ratio between two amounts?The ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
Between two amounts b and a, the ratio is given by the division of b by a, as follows:
r = b/a.
This means that the ratio between two amounts is not commutative, meaning that the order of the amounts matters.
A ladybug with 2 eyes and 6 spots, hence the first sentence is given as follows:
There are 6 spots for every 2 eyes. (ratio is the number of eyes for 6 spots).
The number of spots per eye is the ratio of the number of spots and the number of eyes, as follows:
Spots per eye = 6 spots/2 eyes = 3 spots per 1 eye.
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A rectangular carpet measures 10 m by 6 m
Part of the carpet is covered by a square rug of length 2m
What fraction of the carpet is
covered by the rug?
Give your answer in its simplest form.
Optional working
Answer:
Answer:
Step-by-step explanation:
A rectangular carpet measures 8 m by 6 mPart of the carpet is covered by a square rug of length 2 m
What is the volume of the cube below?
A. 4x2
B. 16
C. 4x
D. 16x2
Answer:
a.
Step-by-step explanation:
The volume of cube 4x².
What is Volume?Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.
We have,
Edges of cube as = 4 , x and x.
So, volume of cube
= 4 x (x . x)
= 4 . x²
= 4x²
Thus, the volume of cube 4x².
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if y1 , y2 , . . . , yn denote a random sample from the normal distribution with mean μ and variance σ2, find the method-of-moments estimators of μ and σ2.
According to normal distribution, the method-of-moments estimators of μ and σ² is (y1 - Y)² + (y2 - Y)² + ... + (yn - Y)²)/(n-1)
The method of moments is a technique used to estimate the parameters of a distribution by equating the sample moments with the theoretical moments. In this case, we want to estimate the mean and variance of the normal distribution using the method of moments.
Let's begin by finding the first moment, which is the expected value or mean of the normal distribution. We can do this by taking the sample mean and equating it with the theoretical mean:
E(Y) = μ
where Y is a random variable from the normal distribution with mean μ and variance σ². The sample mean is given by:
Y = (y1 + y2 + ... + yn) / n
Equating these two expressions, we get:
Y = μ
which gives us our first method of moments estimator for μ.
Next, we can find the second moment, which is the expected value of the square of the random variable. This is related to the variance of the distribution:
E(Y²) = σ² + μ²
Again, we can use the sample moment to estimate the theoretical moment. The sample moment for the second moment is:
Y² + S² = (y1² + y2² + ... + yn²)/n + ((y1 - Y)² + (y2 - Y)² + ... + (yn - Y)²)/(n-1)
where S² is the sample variance. Equating this with the theoretical second moment, we get:
Y² + S² = σ² + μ²
Rearranging this equation, we get our second method of moments estimator:
S² = Y² - μ²
Substituting the first method of moments estimator into this equation, we get:
S² = Y² - Y²
which simplifies to:
S² = (y1 - Y)² + (y2 - Y)² + ... + (yn - Y)²)/(n-1)
This gives us our method of moments estimator for σ².
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Which of the following proves these triangles are congruent?
A - Neither
B - SAA
C - ASA
The statement that proves the congruency of the two triangles is (c) ASA
The given parameter is the two triangles in the figure
For the angles or the sides of the triangles to be congruent, the sides or the angles must be marked with the same identifier
Using the above as a guide,
Two corresponding angles in the triangles are marked with the same symbol
This is represented as AA i.e. Angle-Angle
Also, the triangles share a common side length
This is represented with S i.e. Side
This common side length is between the angles
So, we have
ASA i.e. Angle Side Angle
Hence, the congruency of the two triangles is by the ASA congruent theorem
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A man walks for 45 minutes at a rate of 3 mi/h then jogs for 75 minutes at a rate of 5 mi/h then rests for 30 minutes and finally walks for 90 minutes at a rate of 3 mi/h. Write a piecewise-defined function expressing the distance he traveled as a function of time.
Answer:
Step-by-step explanation:
This is a piece-wise function.
The distance function depends on what time period is involved.
From t=0 to t=0.75, the distance function is: .3t
. . By the end of the 45 minutes, he has gone 2.25 miles.
From t=0.75 to t=2, the distance function is: .2.25+5t
. . By the end of the 75 minutes, he has gone another 6.25 miles, a total of 8.5 miles.
From t=2 to t=2.5, the distance function is: .8.5+0t=8.5
. . By the end of the 30 minutes, he hasn't moved; his total is still 8.5 miles.
From t=2.5 to 4, the distance function is: .8.5+3t
. . By the end of the 90 minutes, he has gone another 4.5 miles, a total of 13 miles.
The function would be written like this:
d(t) = 3t 0 ≤ t ≤ 0.75
2.25+5t 0.75≤t<2
8.5 2≤t≤2.5
8.5+3t 2.5<t<4
what are the solutions tolog3x log3(x2 2) = 1 2log3x?x = –2x = –1x = 1x = 2there is no true solution.
To determine the solutions x⁵ + 2x³ = 3, you can use numerical methods or approximation techniques to estimate the values of x that satisfy the equation.
Let's solve the equation step by step to find the solutions.
Starting with the given equation:
log₃(x) + log₃(x² + 2) = 1 - 2log₃(x)
Now, let's simplify the equation using logarithmic properties. The sum of logarithms is equal to the logarithm of the product, and the difference of logarithms is equal to the logarithm of the quotient:
log₃(x(x² + 2)) = 1 - log₃(x²)
Next, we can simplify further by using the properties of exponents. The logarithmic equation can be rewritten in exponential form as:
(\(3^{(log3(x(x^{2} +2)))} = 3^{(1-log3((x^{2}))}\)
The base of the logarithm and the exponent cancel each other out, resulting in:
x(x² + 2) = \(3^{(1-log3(x^{2}))}\)
Now, let's simplify the right-hand side by applying the power rule of logarithms:
x(x² + 2) = 3 / \(3^{(log3(x^{2} ))}\)
Since \(3^{(log3(x^{2} ))}\) is equal to x² by the definition of logarithms, the equation becomes:
x(x² + 2) = 3 / x²
Expanding the left-hand side:
x³ + 2x = 3 / x²
Multiplying through by x² to eliminate the fraction:
x⁵ + 2x³ = 3
This is a quadratic equation, which does not have a general algebraic solution that can be expressed in terms of radicals. Therefore, it is challenging to find the exact solutions analytically.
To determine the solutions, you can use numerical methods or approximation techniques to estimate the values of x that satisfy the equation.
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Can you help me solve this?
Y-intercept= 4, goes through the point (2, 3)
Please solve using y=Mx+b
Answer:
y=-1/2x+4 Is your answer
Step-by-step explanation:
y=mx+b
3=2x+4
-1=2x
x=-1/2
You already know y is 4 so y=-1/2x+4
The length of a square park is 6 miles. What is the area of the park?
Answer:
36 miles.......................
4. Calculate the values for the ASN curves for the single sampling plan \( n=80, c=3 \) and the equally effective double sampling plan \( n_{1}=50, c_{1}=1, r_{1}=4, n_{2}=50, c_{2}=4 \), and \( r_{2}
Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48
The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:
Single Sampling Plan (n=80, c=3):
ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79
Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):
ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48
The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.
For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.
For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.
These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.
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What is the equation of the line that passes through the point (4, 6) and has an
undefined slope?
Answer:
x = 4
Step-by-step explanation:
a line with an undefined slope is a vertical line parallel to the y- axis, with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (4, 6 ) with x- coordinate 4 , then
x = 4 ← equation of line
The perimeter of a triangle is 16√7 feet. If two of the sides measure √343 feet and √175, find the length of the third side as a radical in simplest form.
Answer:
5√7 feet-------------------
Given:
The perimeter of a triangle - 16√7 feet,Two of the sides - √343 feet and √175 feet.First, convert the two side length as below:
√343 = √(49*7) = 7√7,√175 = √(25*7) = 5√7.Now find the third side:
17√7 - (7√7 + 5√7) = 17√7 - 12√7 = 5√7Hence the third side is 5√7 feet.
The newborn death rate is calculated by dividing the number of newborn deaths by _____ and multiplying by 100.
The newborn death rate is calculated by dividing the number of newborn deaths by the number of live births and multiplying by 100.
The newborn death rate, also known as the neonatal mortality rate, is a critical indicator used in public health to assess the health and well-being of newborns. It is calculated by dividing the number of newborn deaths within a specified period by the number of live births during the same period and then multiplying the result by 100.
This calculation is performed to express the newborn death rate as a percentage, making it easier to interpret and compare across different populations or time periods. By dividing the number of deaths by the number of live births, we obtain the proportion of newborns who die within a certain timeframe. Multiplying this proportion by 100 provides the rate per 100 live births, which allows for a standardized measure of comparison.
The newborn death rate is a crucial statistic in assessing the quality of healthcare services, identifying areas with high mortality rates, and monitoring the effectiveness of interventions aimed at reducing neonatal deaths. It serves as a vital tool for policymakers, healthcare professionals, and researchers in evaluating and improving newborn health outcomes.
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16 oranges and 13 lemons cost $9.29 while 19 oranges and 6 lemons cost $9.05. a pair of equations appropriate for determining the price of each is:
Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.
To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29
This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05
This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.
By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.
One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:
304x + 247y = 176.51
-304x - 96y = -144.8
Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41
So the cost of one orange is $0.41 and the cost of one lemon is $0.21.
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Please answer for brainliest!!!Find the equation of a line that passes through the point (-2,1) and has a gradient of 3. Leave your answer in the form ax+by=c Where a, b and c are integers
Answer:
3x - y = - 7
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 3 and (a, b) = (- 2, 1) , thus
y - 1 = 3(x + 2) ← distribute
y - 1 = 3x + 6 ( subtract 6 from both sides )
y - 7 = 3x ( subtract y from both sides )
- 7 = 3x - y, that is
3x - y = - 7 ← in standard form
Choose the statement that best describes a solution of a system of linear inequalities.(1 point)
A solution of a system of linear inequalities is an ordered pair that satisfies at least one of the inequalities in the system.
A solution of a system of linear inequalities is an ordered pair that satisfies the intersection of the border of each inequality.
A solution of a system of linear inequalities is an ordered pair that satisfies neither inequality in the system.
A solution of a system of linear inequalities is an ordered pair that satisfies each inequality in the system.
Answer: A solution of a system of linear inequalities is an ordered pair that satisfies each inequality in the system.
Step-by-step explanation:
A system of linear inequalities can be written as:
y < a*x + b
y < c*x + d
or
y ≤ a*x + b
y ≤ c*x + d
In the first case, the borders are not included in the solutions, and in the second case, the borders are included.
Where the solutions will be points like (x, y), where these points must be solutions for both inequalities.
Then the only option that is correct for a general system of inequalities is:
A solution of a system of linear inequalities is an ordered pair that satisfies each inequality in the system.
Answer:
A solution of a system of linear inequalities is an ordered pair that satisfies at least one of the inequalities in the system.A solution of a system of linear inequalities is an ordered pair that satisfies the intersection of the border of each inequality.A solution of a system of linear inequalities is an ordered pair that satisfies neither inequality in the system.A solution of a system of linear inequalities is an ordered pair that satisfies each inequality in the system.
If Cos A = 9/41 and tan B = 28/45 angle A and B are in quadrant I find the value of Tan(A+B)
The amount of pages Ashlyn read last night is 24.
This is 10% of the entire book. How many pages
are in the book?
Answer:
240 pages
Step-by-step explanation:
1. To find the total number of pages in the book, we can use this equation: \(\frac{10}{100}x = 24\) .
This equation means that 10% of something = 24, which correctly represents out situation.2. (Solving)
Step 1: Simplify both sides of the equation.
\(\frac{10}{100}x = 24\) \(\frac{1}{10}x=24\)Step 2: Multiply both sides by 10.
\(\frac{1}{10}x * 10 = 24 * 10\) \(x = 240\)Therefore, the answer is 240 pages.
Compared to a z-score, a hypothesis test with a t statistic requires more information from the sample.
a) True
b) False
The statement is b) False. A hypothesis test with a t statistic does not require more information from the sample; it utilizes different information and assumptions compared to a z-score depending on the characteristics of the data.
A hypothesis test with a t statistic does not require more information from the sample compared to a z-score. In fact, the t statistic is used when the sample size is small or when the population standard deviation is unknown, whereas the z-score is used when the sample size is large and the population standard deviation is known.
In hypothesis testing, both z-tests and t-tests are used to make inferences about a population based on sample data. The main difference between them lies in the assumptions made about the population standard deviation.
In a z-test, the population standard deviation is known and used in the calculation of the test statistic, which follows a standard normal distribution. Therefore, it requires knowledge of the population standard deviation.
On the other hand, in a t-test, the population standard deviation is unknown and estimated using the sample standard deviation. The test statistic in a t-test follows a t-distribution, which takes into account the variability introduced by the estimation of the population standard deviation. Hence, it requires less information about the population compared to a z-test.
The t statistic takes into account the sample size and the sample standard deviation to estimate the population parameters, while the z-score uses the known population parameters. Therefore, the t statistic provides a more accurate inference when the sample size is small or when the population standard deviation is unknown.
In conclusion, a hypothesis test with a t statistic does not require more information from the sample; it utilizes different information and assumptions compared to a z-score depending on the characteristics of the data.
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Find the volume of a triangular prism where the base length is 6 ft, the base height is 5 ft, and the prism height is 7 ft.
Given:
The base length is 6 ft, the base height is 5 ft, and the prism height is 7 ft.
To find:
The volume of the triangular prism.
Solution:
Base of a triangular prism is a triangle with base length 6ft and height 5 ft.
Area of a triangle is
\(Area=\dfrac{1}{2}\times Base\times Height\)
So, the area of the base is
\(B=\dfrac{1}{2}\times 6\times 5\)
\(B=\dfrac{30}{2}\)
\(B=15\)
Now, the volume of a triangular prism is
\(V=Bh\)
Where, B is the base area and h is the height of the prism.
Putting B=15 and h=7, we get
\(V=(15)(7)\)
\(V=105\)
Therefore, the volume of the triangular prism is 105 cubic ft.
GIVING BRAINLIEST, NO LINKS, LOOK AT THE PICTURE
Answer: 2 2/5
Step-by-step explanation:
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Today the population of a city is 250,000 and is growing at a rate
of 4% per year. When or how many years will the population reach
850,000
Step-by-step explanation:
Principal = 250,000
Rate = 4%
Simple interest = 850,000
Time = ?
\(t = \frac{100 \times interest}{principal \times rate} \\ t = \frac{100 \times 850000}{250000 \times 4} \\ t = \frac{100 \times 85}{25 \times 4} \\ t = \frac{8500}{100} \\ t = 85years\)
Layla earned an 80% on a recent math
quiz. She scored 16 points. How many
total points were there on the quiz?
I think it might be 20???