The height from the ground to the top of the ladder is 61. 28 feet
How to determine the heightFirst, we need to know that their are six different trigonometric identities.
These identities includes;
secantcotangenttangentcosinesinecosecantFrom the information given, we have that;
the height of the ladder that is leaning against the house = 80 feet
This the hypotenuse side
The angle of elevation is 50 degrees
Then, the opposite side is the height from the ladder = x
Using the sine identity, we have;
sin 50 = x/80
cross multiply the values
x = 61. 28 feet
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Help me please I don’t understand
Answer:16x-4-2x+8=14x+4
Step-by-step explanation:
In order to solve this question you first want to multiply everything inside the bracket by the number outside.
4(4x-1)
so 4 times 4x which is 16x and 4 times -1 which is -4 so the first bracket is
(16x-4)
then do the same for the second bracket
-2(x-4)
so -2 times x would be -2x and -2 times -4 would be 8
for the final step collect the like terms and solve
so your answer would be
16x-2x which would be 14x and -4+8 which would be 4
so in conclusion the answer is
14x+4
log3 55=x
Use the base of formula to solve for x in logaritm experssion
The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.
The logarithmic expression given is
log₃ 55 = x
To solve for x using the change of base formula, we can use the formula
logₐ b = log c / log a
where a, b, and c are positive real numbers and a ≠ 1.
Using this formula, we can rewrite the given expression as
log x / log 3 = log 55 / log 3
We can simplify this expression by canceling out log 3 on both sides
log x = log 55
Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get
x = 55
Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.
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Find the probability the student is a sophomore.
Answer:
I believe the answer is 30%
Hurry pls (Time limit)
Give me the domain and range
Tell me if the graph is a function or not.
The answer choices are below
The graph is a function: yes.
The domain of this function is: all real numbers.
The range of this function: all real numbers.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞}, x|x ∈ R, or all real numbers.
Range = {-∞, ∞}, y|y ∈ R, or all real numbers.
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Given g(x)=x²-6x-16, which statement is true?
The zeros are -8 and 2, because the factors of gare (x+8) and (x-2).
The zeros are -8 and -2, because the factors of g are (x + 8) and(x+2).
The zeros are -2 and 8, because the factors of gare (x+2) and (x-
8).
The zeros are 2 and 8, because the factors of gare (x-2) and (x-
8).
Since g(x) = x² - 6x - 16, a statement which is true include the following: C. The zeros are -2 and 8, because the factors of g are (x+2) and (x-
8).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
g(x) = x² - 6x - 16
0 = x² - 6x - 16
0 = x² - 8x + 2x - 16
0 = x(x - 8) + 2(x - 8)
(x - 8)(x + 2)
x = 8 or x = -2.
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Sera is solving a number puzzle that involves three integers e, f, and g where e is negative. The product of e and f is-12. The product of e and g is 6. The product of f and g is -8. What are the values for e, f, and g?
The values for e, f, and g are -3, 4 and -2 respectively.
What are the values for e, f, and g?e × f = -12
e × g = 6
f × g = -8
From (1)
ef = -12
e = -12/f
From (3)
fg = -8
g = -8/f
Substitute e and g into (2)
e × g = 6
-12/f × -8/f = 6
96/f² = 6
cross product
96 = f² × 6
96 = 6f²
divide both sides by 6
f² = 96/6
f² = 16
find the square root of both sides
f = √16
f = 4
Hence,
e × f = -12
e × 4 = -12
4e = -12
e = -12/4
e = -3
e × g = 6
-3 × g = 6
-3g = 6
g = 6/-3
g = -2
f × g = -8
4 × -2 = -8
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A student argues that y=x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student? Explain why.
The student's argument that y=x/9 does not represent a proportional relationship between x and y is false because there is constant factor which shows the proportional relationship.
A proportional relationship exists between two variables if they are related by a constant factor, meaning that multiplying one variable by a constant results in the other variable. However, this constant can also be obtained by dividing one variable by the other, as in the case of y=x/9.
To see why, we can rearrange the equation to x=9y, which shows that x is proportional to y with a constant factor of 9. Multiplying y by 9 results in x, just as dividing x by 9 results in y. Therefore, the relationship between x and y is still proportional, regardless of whether we multiply or divide to obtain the constant factor.
In general, we can say that a relationship between two variables is proportional if it can be written in the form y=kx, where k is a constant. It does not matter whether we use multiplication or division to express this constant, as long as it is the same for all values of x and y.
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Round 2,561 to the nearest hundred.
Answer:
2,600.
Step-by-step explanation:
Rounding 2,561 to the nearest hundred means rounding it to the nearest multiple of 100.
To do this, we need to look at the digit in the tens place, which is 6. Since 6 is greater than or equal to 5, we round up the digit in the hundreds place, which is 25, by 1.
Therefore, rounding 2,561 to the nearest hundred gives us 2,600.
A company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year. If bonds are sold at par value, the issuer records the first semi-annual interest payment with a credit to in the amount of $ .
The first semi-annual interest payment with a credit to in the amount of $109.556.15
Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.
We need to find the amount,
[tex]A = P(1+r/2)^{2t}[/tex]
[tex]A = 50,000(1+0.08/2)^{2(10)[/tex]
[tex]A = 50,000(1.04)^{20[/tex]
[tex]A = 109,556.15[/tex]
Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15
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.54 oz of premium walnuts costs $12.95. what is cost per ounce
The cost per ounce of the premium walnut is $0. 23
What is proportion?To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such that they are made equal to another.
From the information given, we have that;
54 ounces of premium walnuts costs $12.95
This is represented as;
54 ounces = $12. 95
Then 1 = x
cross multiply the values, we get;
x = $12.95/54
Divide the values, we get;
x = $0. 23
Hence, the value is $0. 23 per premium walnut
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Find the area of the composite figure.
2 ft
F
4.5 ft
K
6.5 ft
1 ft
1 ft
The area of the composite figure is 13 ft².
How to find the area of a composite figure?The figure is a composite figure. The are of the composite figure is the sum of the individual areas.
The composite figure can be divided into two shapes namely rectangle and triangle.
Therefore,
area of the composite figure = area of the rectangle + area of the triangle
Hence,
area of the rectangle = 4.5 × 2
area of the rectangle = 9 ft²
area of the triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × 4 × 2
area of the triangle = 8 / 2
area of the triangle = 4 ft²
Therefore,
area of the composite figure = 9 + 4
area of the composite figure = 13 ft²
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Find and compare the domain and range of each function. f(x) = 5/8x + 1 g(x) = 2/3x^3 A. The domains and ranges of both functions are not restricted. B. The domain of f is restricted, but its range is not. The domain and range of g are not restricted. C. The range of f is restricted, but its domain is not. The domain and range of g are not restricted. D. Both the domain and range of f are restricted, but the domain and range of g are not.
A. The domains and ranges of both functions are not restricted.
For f(x) = 5/8x + 1, any real number can be plugged in for x, so the domain is (-∞, ∞). Similarly, any real number can be obtained by evaluating the function, so the range is also (-∞, ∞).
For g(x) = 2/3x^3, any real number can be plugged in for x, so the domain is (-∞, ∞). As x is cubed, the range can be negative or positive infinity, or any real number in between, so the range is also (-∞, ∞).
Therefore, both functions have unrestricted domains and ranges.
The correct answer is A.
Select the correct answer.
A glass case is in the shape of a rectangular prism. The volume of the case is cubic foot. How many cubic blocks with a side length of foot would
be required to find the volume of the glass case?
OA 2
OB 3
OC. 4
D. 5
Reset
From the question that we have, the solution that we have gotten is that 4 cubic blocks with a side length of foot would be required to find the volume of the glass case
How to solve the problemWe have been given that a glass case is in shape of a rectangular prism.
The volume of a single cubic block is:
We have
Volume of block
= (1/5) * (1/5) * (1/5)
= 1/125 cubic feet
Next we will now have to divide the volume of the glass case by the volume of a single cubic block:
V olume of case / Volume of the block =
(4/125) / (1/125)
= 4
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A glass case is in the shape of a rectangular prism. The volume of the case is cubic 4/125 foot. How many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case?
Fill in the paragraph shown with the correct information from the answer choices provided.
Portland Rainfall
Seattle Rainfall
(inches)
(inches)
4
3
2
Week
1
2
3
4
5
5
10
1
4
7
6
5
A meteorologist tracks the rainfall in two cities.
variability
By calculating the
claim that Portland tends to receive more rainfall than Seattle.
of the data, the meteorologist can
mean
By calculating the median of the data, the meteorologist can claim that Portland tends to receive more rainfall than Seattle.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
The ordered data-sets for each city are given as follows:
The median is the middle element for each data-set, hence it is given as follows:
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simplify the following expression:
(2x^3)^2 * (3x)^4
[tex](2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}[/tex]
Given the polynomial 9x2y6 − 25x4y8, rewrite as a product of polynomials.
(9xy3 − 25x2y4)(xy3 + x2y4)
(9xy3 − 25x2y4)(xy3 − x2y4)
(3xy3 − 5x2y4)(3xy3 + 5x2y4)
(3xy3 − 5x2y4)(3xy3 − 5x2y4)
The polynomial can be written as a product of polynomials as (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)
option C.
What is the product of the polynomial?To rewrite the polynomial as the product of its form, we will factor the polynomial as shown below;
9x²y⁶ − 25x⁴y⁸ = x²y⁶(9 − 25x²y²)
The function (9 − 25x²y²), can factored using difference of two squares;
(9 − 25x²y²) = 3² − (5xy)²
3² − (5xy)² = (3 - 5xy)(3 + 5xy)
The final equation as the product of its factors is calculated as;
9x²y⁶ − 25x⁴y⁸ = x²y⁶(3 - 5xy)(3 + 5xy)
= (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)
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Ethan correctly answers 80% of the total questions on his history test. He correctly answers 32 questions.
Answer: There are 40 questions on Ethan's test.
Step-by-step explanation: To find what 32 is 80% of, you must first convert 80% to a decimal (.8).
Next, divide 32 by .8.
[tex]32/.8 = 40[/tex]
Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points) Group of answer choices x = 2 x = 3 x = 5 x = 6
#3 i
Cylinder A and Cylinder B are similar. Find the surface area of Cylinder B. Give your answer in terms of pi.
The volume of the small cylinder is 36π
What are similar shapes?Similar figures are two figures having the same shape. The two cylinders are similar but of different radius and height.
The height of the big cylinder is calculated as
V = πr²h
h = V/ πr²
h = 144π/π36
h = 144/36
h = 4 cm
Therefore the scale factor = 4/2
area factor =( 4/2)² = 16/4
therefore the volume of the cylinder is;
16/4 = 144π/ x
16x = 144π × 4
16x = 576
dividing both sides by 16
x = 576/16
x = 36π
therefore the volume of the small cylinder is 36π.
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Which of these fractions is largest A: 6 as a fraction of 30 B: 30 centimetres as a fraction of 2 metres C: 16 pence as a fraction of £1 ? You must show your working.
Answer:
A: 6 as a fraction of 30 = 6/30 = 1/5
B: 30 centimetres as a fraction of 2 metres = 30/200 = 3/20
C: 16 pence as a fraction of £1 = 16/100 = 4/25
To compare these fractions, we need to express them with a common denominator. The smallest common multiple of 5, 20, and 25 is 100. So we can convert each fraction to have a denominator of 100:
A: 1/5 = 20/100
B: 3/20 = 15/100
C: 4/25 = 16/100
Now we can see that the largest fraction is C: 16 pence as a fraction of £1, which is 16/100 or 16%.
Step-by-step explanation:
Mark Brainliest!!
710 divided by 9
what is the answer please help
Answer:
78.8888888889 or just round to 79
Step-by-step explanation:
Your welcome. Can you please mark me brainliest please? :)
Answer:
78.8888888889
Step-by-step explanation:
Will give Brainliest and points!!!!
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
The slope of the line and its meaning in terms of the real-world scenario is; C. The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
How to calculate or determine the rate of change or slope of a line?In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 24)/(6 - 0)
Slope (m) = -24/6
Slope (m) = -4.
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please help me with this.
According to the figure,
a. angle LCQ is 45 degrees
b. the major arc are KPR and QRPK
c. congruent minor arcs are LQ and QR
d. the three arcs that form a semicircle are RP, LQ ,and QR
What are major arcs?A major arc designates a segment of an arch with a measurement which surpasses 180 degrees.
Geometrically, the circle, a closed curve, exhibits all its points uniformly spaced from a central focal point named the center of the circle.
The arc is regarded as major when it comprises a superior portion of the circular geometry, extending beyond half of the total circumference.
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Martina vence a Jelena en 2 juegos de un total de 3 en el tenis. ¿Cuál es la probabilidad de que Jelena gane un set de de tenis 6 juegos a 4?
Pista: ¿Cuál es el score que tendría que haber después de 9 juegos?
0.034141137 o sobre 17/500
1
2
32
1 point
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
The value of the median for this data set would be type your answer....
1 point
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
The value of the mode for this data set would be type your answer.....
1 point
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
The value of the mean for this data set would be type your answer....
(Input only a number)
(Input only a number)
(Input only a number)
AnswerAnswer:
55
60
57.27
Step-by-step explanation:
rearrange the values in order:
40, 45, 45, 50, 50, 55, 60, 60, 60, 95, 100
1. median is the middle number when we put all the numbers in order, and it is 55 for this list.
2. mode is the number that appears the most, and in this list, it's 45 and 60.
3. mean is the average of all the scores in the list, and it's 57.27 for this list.
chatgpt
If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where it is the
number of years from today.
P (0)=1200 (1.026)
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.
Current price $?
Price from 8 years from today$?
Answer: the price of the item 8 years from today is approximately $1475.
Step-by-step explanation:
The given exponential function to model the future price of the item is:
P(t) = P(0) * (1.026)^t
Here, P(t) represents the price of the item t years from today, and P(0) is the current price of the item.
1. To find the current price, we need to find P(0):
P(0) = 1200 * (1.026)^0
Since any number raised to the power of 0 is 1:
P(0) = 1200 * 1
P(0) = $1200
So, the current price of the item is $1200.
2. To find the price 8 years from today, we need to find P(8):
P(8) = 1200 * (1.026)^8
Using a calculator:
P(8) ≈ 1200 * 1.229057
P(8) ≈ $1474.87
Rounded to the nearest dollar:
P(8) ≈ $1475
So, the price of the item 8 years from today is approximately $1475.
The graph of f(x) is shown below. - NW544 -3 (0.6) 2 1 -6-5-4-3-2-11 7 7 7 7 9 9 2 4 1 2 3 4 5 6 x If f(x) and its inverse function, f¹(x), are both plotted on the same coordinate plane, where is their point of intersection?
The point of intersection between a Inverse Functions and its inverse occurs at (2, 2).
The point of intersection between a function and its inverse occurs when the input and output values are the same for both functions.
To find the point of intersection, we need to find the value of x where f(x) = f-1(x).
In this particular case, we can see from the graph that the point of intersection occurs at (2, 2).
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The average student at Rio Hondo takes 9.1 units per semester (SD = 1.2). Some people believe that students in transfer level math will be more likely to be on track to graduate quickly. Five students from PSY 190 were taking 12, 14, 6, 6, and 16 units. Conduct the steps of hypothesis testing to determine whether students in PSY 190 take more units compared to the average Rio Hondo student.
The critical value from the given data is 2.776.
Hypothesis Testing:
Step 1: State the null and alternative hypotheses.
Null Hypothesis (H0): The average number of units taken by students in PSY 190 is equal to the average number of units taken by Rio Hondo students.
Alternative Hypothesis (H1): The average number of units taken by students in PSY 190 is greater than the average number of units taken by Rio Hondo students.
Step 2: Calculate a test statistic.
To calculate a test statistic, we will use a one-sample t-test. The t-test will allow us to compare the average of the PSY 190 students to the average of all Rio Hondo students. The test statistic will be calculated as follows:
t = (x - μ) / (s/√n)
Where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
In this case, x = 10.6, μ = 9.1, s = 5.1, and n = 5.
Plugging these values into the equation, we get:
t = (10.6 - 9.1) / (5.1/√5) = 1.78
Step 3: Determine the critical value.
To determine the critical value, we need to determine the degrees of freedom, which is equal to n-1 = 4. We can then look up the critical value in a t-table with α = 0.05 and 4 degrees of freedom. The critical value is 2.776.
Step 4: Compare the test statistic to the critical value.
Since the test statistic (1.78) is less than the critical value (2.776), we fail to reject the null hypothesis.
Therefore, the critical value from the given data is 2.776.
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
415.67 = (1/3)(13.4)(11.7)h
415.67 = 52.26h
h = about 7.95 feet
What is the next term in the pattern? 1,1,5,17,71,247
Answer: 1085
Step-by-step explanation: