Find the value of x. Round your answer to the nearest tenth. Show your work please!
Answers
cos(Ф)=adjacent/hypotenuse
cos(22°)=x/11
11 · cos(22°)= x/11 · 11 multiplicative inverse
11 cos (22°)=x
10.2≈x
Related Questions
two crooks rob a bank and flee to the east at 66mph. in 30 minutes, the police follow them in a helicopter, flying 132mph. how long will it take for police to overtake the robbers?
Answers
To calculate this, firstly we need the initial lead of the robbers in miles before the police starts to chase, which is the product of the speed of the robbers and the time before the police starts to chase. Given that the speed of robbers is 66 mph and the time before the police chase is 0.5 hours, multiplying these gives a robber lead of 33 miles.
Next, to determine how quickly the police can close this gap, we need to calculate the relative speed of the police helicopter compared to the robbers. The speed of the police is 132 mph and the speed of the robbers is 66 mph, the difference between these two speeds is the relative speed. So, 132 mph - 66 mph gives a relative speed of 66 mph.
Finally, the time it will take for the police to catch up to the robbers - the catchup time - is the ratio of the initial lead of the robbers to the relative speed of the police. Here it is 33 miles divided by 66 mph, this yields a catchup time of 0.5 hours.
Therefore, it will take the police 0.5 hours to overtake the robbers.
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Which equation is equivalent toy- 6 = -12(x+ 4)? (1 point)
a. y=-6x-48
b. y=6x-48
c. y=-12x-42
d. y=-12x-54?
Answers
y=-12x-48+6
y=-12x-42
choose the ratio that you would use to convert 2.5 centimeters to meters please
Answers
The ratio which is used to convert 2.5 centimeters to meters is : (d) 1 meter/100 centimeter.
To convert 2.5 centimeters to meters, we choose the ratio that relates centimeters to meters,
The correct ratio to use in this case is 1 meter/100 centimeters,
This ratio states that there are 100 centimeters in 1 meter.
To convert centimeters to meters, we divide the given measurement (2.5 centimeters) by the ratio of 1 meter/100 centimeters.
Using this ratio, we have:
2.5 centimeters × (1 meter/100 centimeters) = 2.5/100 meters
2.5/100 = 0.025 meters,
So, 2.5 centimeters is equal to 0.025 meters.
Therefore, The correct answer is (d) 1 meter/100 centimeter.
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How can you display data in a Histogram?
Answers
Answer:
You can display data in a histogram by labeling the x and y axis with your numbers provided. Then you put in the amount of numbers.
Answer:
Sample response: To create a histogram, first label the x-axis and choose the interval. Then calculate the frequency of each interval. Next, label the y-axis and determine the scale. Now create the bars. Draw bars the height of the frequency for each interval. Last, give the graph a title.
Step-by-step explanation:
Angela uses 2/3 cup strawberries to make 5/6 of a liter of smoothies what is unit rate in cups of strawberry per liter
Answers
Answer:
[tex]\frac{4}{5}\frac{cup}{liter}.[/tex]
Step-by-step explanation:
The problem says that Angela uses 2/3 cup strawberries to make 5/6 liter of smoothies. Then, to find the unit rate in cups of strawberrry per liter, that is cup/liter we need to divide both fractions:
[tex]\frac{\frac{2}{3}cup}{\frac{5}{6}liter} = \frac{2*6}{3*5}\frac{cup}{liter} = \frac{12}{15}\frac{cup}{liter}= \frac{4}{5}\frac{cup}{liter}.[/tex]
Then, the unit rate in cups of strawberry per liter is [tex]\frac{4}{5}\frac{cup}{liter}.[/tex] That is, Angela uses 4/5 cups of strawberry to do 1 liter of smoothie.
A cereal bar contains 4000 milligrams of protein. How much protein does it contain in grams
Answers
Please please please please help me out.
What is the volume of the item described?
A capsule consisting of a cylinder of radius 3 mm and height 6 mm with a hemisphere on each end of radius 3 mm.
Answers
Answer:
90 and 283
Step-by-step explanation:
Find a basis for the row space and column space of a matrix and the rank .
Answers
Final answer:
To identify a basis for the row and column spaces of a matrix and determine its rank, one uses row reduction to reach REF or RREF. The non-zero rows of the RREF are the basis for the row space, the corresponding columns in the original matrix form the basis for the column space, and the rank is the number of these basis vectors. In statistics, the degrees of freedom for the Test of Independence is calculated as (number of columns - 1)(number of rows - 1).
Explanation:
To find a basis for the row space and column space of a matrix as well as the rank, you follow specific procedures. First, perform row reduction on the matrix to bring it to row echelon form (REF) or reduced row echelon form (RREF). The non-zero rows of the RREF correspond to a basis for the row space. The columns in the original matrix that correspond to the leading 1s in the RREF form a basis for the column space. The rank of the matrix is equal to the number of leading 1s in the RREF form, which is also the number of basis vectors for either the row space or column space since they have the same dimension.
The Test of Independence in statistics uses a contingency table to determine if two categorical variables are independent. The number of degrees of freedom for the test is given by the formula: (number of columns - 1)(number of rows - 1). This is critical when referencing the chi-squared distribution table to determine the p-value for the hypothesis test.
What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test (to 4 decimals)? 0.6578?
Answers
Critical Reading 502
Mathematics 515
Writing 494
Assume that the population standard deviation on each part of the test is σ = 100.
We find the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test (to 4 decimals) as follows:
Within 10 points of 502 implies (502 - 10, 502 + 10) = (492, 512).
Because the sample is large, we assume normal distribution.
The probability that the mean statistic of sample data is between two points (a, b) is given by:
[tex]P(a\ \textless \ \bar{x}\ \textless \ b)=P\left( \frac{b-\mu}{\sigma/\sqrt{n}} \right)-P\left( \frac{a-\mu}{\sigma/\sqrt{n}} \right)[/tex]
Thus,
[tex]P(492\ \textless \ \bar{x}\ \textless \ 512)=P\left( \frac{512-502}{100/\sqrt{90}} \right)-P\left( \frac{492-512}{100/\sqrt{90}} \right) \\ \\ = P\left(\frac{10}{10.5409} \right)-P\left(\frac{-10}{10.5409} \right)=P(0.9487)-P(-0.9487) \\ \\ =P(0.9487)-[1-P(0.9487)]=2P(0.9487)-1=2(0.82861)-1 \\ \\ =1.65722-1=0.65722[/tex]
Therefore, the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test (to 4 decimals) is 0.6572.
The probability that the sample mean of 90 test takers falls within 10 points of the population mean of 502 is approximately 0.6578.
To find the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test, we need to calculate the probability using the standard normal distribution.
Given:
- Population mean [tex](\(\mu\))[/tex]: 502
- Sample size[tex](\(n\))[/tex]: 90
- Standard deviation [tex](\(\sigma\))[/tex] of the population (assumed known or provided): Let's assume it is 100 (for example purposes).
We are looking for the probability that the sample mean[tex](\(\bar{X}\))[/tex] falls within 10 points of the population mean (502 ± 10).
Step 1: Calculate the standard error of the mean (SEM):
[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} \][/tex]
[tex]\[ SEM = \frac{100}{\sqrt{90}} \][/tex]
[tex]\[ SEM = \frac{100}{9.4867} \][/tex]
[tex]\[ SEM \approx 10.548 \][/tex]
Step 2: Convert the deviation of ±10 points from the mean into a z-score using the standard normal distribution:
[tex]\[ z = \frac{\text{sample mean} - \mu}{SEM} \][/tex]
For the upper bound:
[tex]\[ z_{\text{upper}} = \frac{502 + 10 - 502}{10.548} \][/tex]
[tex]\[ z_{\text{upper}} = \frac{10}{10.548} \][/tex]
[tex]\[ z_{\text{upper}} \approx 0.9497 \][/tex]
For the lower bound:
[tex]\[ z_{\text{lower}} = \frac{502 - 10 - 502}{10.548} \][/tex]
[tex]\[ z_{\text{lower}} = \frac{-10}{10.548} \][/tex]
[tex]\[ z_{\text{lower}} \approx -0.9497 \][/tex]
Step 3: Find the cumulative probabilities using the standard normal distribution table or a calculator:
[tex]\[ P(-0.9497 \leq Z \leq 0.9497) \][/tex]
Using a standard normal distribution table or a calculator, find:
[tex]\[ P(Z \leq 0.9497) \approx 0.8289 \][/tex]
[tex]\[ P(Z \leq -0.9497) \approx 0.1711 \][/tex]
Step 4: Calculate the probability that the sample mean falls within 10 points of the population mean:
[tex]\[ P(-0.9497 \leq Z \leq 0.9497) = 0.8289 - 0.1711 \][/tex]
[tex]\[ P(-0.9497 \leq Z \leq 0.9497) = 0.6578 \][/tex]
Therefore, the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 is approximately [tex]{0.6578} \).[/tex]
use the remainder therom to find the remainder when x^4-3x^2-9x+4 is divided by x-3
Answers
[tex]\underbrace{p(x)}_{\text{given}}=q(x)(x-3)+r(x)[/tex]
that is, write [tex]p(x)[/tex] as the product of two factors plus some remainder term, then we can simply plug in [tex]x=3[/tex] to determine the remainder term because that would force the [tex]q(x)[/tex] term to vanish.
[tex]p(x)=x^4-3x^2-9x+4\implies p(3)=31[/tex]
so the remainder upon dividing [tex]p(x)[/tex] by [tex]x-3[/tex] is 31.
Final answer:
To find the remainder when dividing x^4-3x^2-9x+4 by x-3, substitute x=3 into the polynomial and calculate the expression.
Explanation:
To find the remainder when dividing x^4-3x^2-9x+4 by x-3, we can use the Remainder Theorem. According to the theorem, if we substitute the opposite of the divisor into the polynomial, the remainder will be the value we get.
So, substitute x = 3 into the polynomial:
3^4 - 3(3)^2 - 9(3) + 4
Calculating this expression, we find that the remainder is 142.
Solve the equation below for x by graphing. x ≈ -2.50 x ≈ 2.50 x ≈ -0.50 x ≈ -6.00
Answers
Answer:
The answer is A. -2.50
Step-by-step explanation:
A club orders 124 T-Shirts at a cost of $18 each. Which is the best estimate of the total cost of the order?
Answers
We can round 18 to 20, since 20 is easier to multiply.
124 × 20 = 2,480
Because this was an overestimate, the 124 × 18 should be less than 2,480, but close.
Please let me know if my answer was helpful! =)
You have been observing a population of swallowtail butterflies for the last 10 years. the size of the population has varied as follows: 54, 11, 89, 17, 66, 58, 5, 9, 99, and 23. what is the effective population size of this population of butterflies (give your answer as an integer)?
Answers
Two cargo trains each leave their respective stations at 1:00 p.m. and approach each other, one traveling west at 6 miles per hour and the other on separate tracks traveling east at 14 miles per hour. The stations are 40 miles apart. Find the time when the trains meet and determine how far the eastbound train has traveled.
A). 3 p.m, 28 mi
B). 12 p.m., 20 mi
C). 2 p.m., 18 mi.
D). 1 p.m., 15 mi
Answers
let x = hours
6x + 14x = 40
20x=40
x = 40/20 = 2 hours
1 pm + 2 hours = 3 pm
eastbound trains is going 14 miles per hour, 14 mph x 2 hours = 28 miles
Answer is A. 3 pm and 28 miles
The eastbound train has traveled 28 miles and they met at 3:00 pm
Speed is the ratio of total distance to total time taken. It is given by:
Speed = distance / time
Let both cargo trains meet each other at time t.
For the train traveling west:
6 = d₁ / t
d₁ = 6t
For the train traveling east:
14 = d₂ / t
d₂ = 14t
Since both trains are 40 miles apart, hence:
d₁ + d₂ = 40
6t + 14t = 40
20t = 40
t = 2 hours
t = 3:00 pm (1:00 pm + 2 hours)
Distance travel by east bound train = d₂ = 14t = 14(2) = 28 miles
The eastbound train has traveled 28 miles and they met at 3:00 pm
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The Himalayas have an uplift rate of about 2 inches per year. Assuming uplift began 40 million years ago, calculate how high the mountains would be in feet (elevation above sea level) today.
Answers
The current height = 2 * 40,000,000 = 80,000,000 inches
Now, we need to convert the inches to feet as follows:
1 inch = 0.08334 ft, therefore:
height of Himalayas = 6667200 ft
which of the following fraction is more 2/3, 7/8, 1/2, or 3/4
Answers
2/3=16/24
7/8=21/24
1/2=12/24
3/4=18/24
7/8 is the most
what is the indicated operation of
10 3/7 + 19 5/9
Answers
Final answer:
To find the sum of mixed numbers, convert them into improper fractions and then add the fractions together. The answer here is 1889/63.
Explanation:
The student’s question “what is the indicated operation of 10 3/7 + 19 5/9” asks to perform the operation of addition between two mixed numbers. The indicated operation is addition. To add these mixed numbers, you first add the whole numbers (10 + 19) and then add the fractions (3/7 + 5/9). When adding fractions, find a common denominator, in this case, 63, and convert the fractions to have this common denominator before adding.
To find the sum of mixed numbers, we first convert them into improper fractions.
10 3/7 becomes 73/7 and 19 5/9 becomes 176/9.
Then, we add the numerator of the fractions and keep the denominator the same. So, 73/7 + 176/9 = (73 * 9 + 7 * 176)/(7 * 9). Which gives 1889/63.
Which of the following matrices represents the average number of vehicles sold for the two months shown in the table below?
Answers
Here is how you get the answer:
Location A Location B
Truck (129 + 145) / 2 = 137 (94 + 104) / 2 = 99
Car (123 + 101) / 2 = 112 (120 + 142) / 2 = 131
SUV (92 + 128) / 2 = 110 (130 + 134) / 2 = 132
So the matrix is:
137 99
112 131
110 132
what is the unit rate for $240 for 4 days
Answers
$240
---------- = $60/day
4 days
What is the end behavior of the graph of the polynomial function f(x) = 2x^3 – 26x – 24?
Answers
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The graph of f(x) is shown in the attached image. Imagine we can plot a point anywhere on this curve. Also imagine that this point can slide around as if it is a car on a roller coaster track. If the car moves to the left, then it will go downward ultimately. This indicates that
as x approaches -infinity, then y also approaches negative infinity
as [tex]x \to -\infty[/tex] then [tex]y \to -\infty[/tex]
If you move the car to the right then it will move upward. So,
as x approaches positive infinity, then y approaches positive infinity
as [tex]x \to \infty [/tex] then [tex]y \to \infty [/tex]
Combine all of this and that leads to choice B as the final answer
One way to describe this end behavior is:
"Falls to the left and rises to the right"
The end behavior of the function f(x) = 2x³ – 26x – 24 can be described as:
As x → -∞, y →-∞ and as x→∞, y →∞.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
To determine the end behavior of the polynomial function f(x) = 2x³ – 26x – 24, we need to examine the degree of the polynomial and the sign of its leading coefficient.
The degree of the polynomial is 3, which means it is an odd-degree polynomial.
The sign of the leading coefficient is positive (+2). These two pieces of information tell us that the end behavior of the graph will be as follows:
As x becomes very large in the positive direction, the values of the function will also become very large in the positive direction.
As x becomes very large in the negative direction, the values of the function will become very large in the negative direction.
Therefore, as x → -∞, y →-∞ and as x→∞, y →∞.
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A toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles. Suppose that during daytime hours, 65% of all vehicles are passenger cars. If 20 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? [Hint: Let X = the number of passenger cars; then the toll revenue h(X) is a linear function of X.]
Answers
this means that 65% of 20 are passenger cars..
0.65(20) = 13 cars are passenger cars.....leaving (20 - 13) = 7 that are other vehicles.
toll bridge charges $ 1 for passenger cars and 2.50 for other vehicles...
expected toll revenue is : 13(1) + 7(2.50) = 13 + 17.5 = $ 30.50 <==
plez help me and show your work
Answers
0.7/10 = 0.07
1.05 / 15 = 0.07
1.40 / 20 =0.07
1.75/25 = 0.07
yes it is proportional ( they all equal the same when divided)
proportion = 0.07
Part B) y = 0.07x
Write the expanded form using fraction or decimal 24.357
Answers
24.357 in expanded form is, 24×1 next 3× 1/10 then 5× 1/100 and finally 7× 1/1000
Hoped this helped! If you have any questions just ask! I am here to help.
The perimeter of a rectangular garden is 90 meters. the length is 6 meters longer than twice the width. find the dimensions of the garden.
Answers
The formula for the Perimeter of a rectange is P = 2L + 2W.
Here, P = 2(2W + 6) + 2W = 90 (all dimensions in meters).
Then 4W + 12 + 2W = 90; 6W = 78; W=13 meters. Then L = 2W + 6=
2(13) + 6 = 32 meters.
Check: Does P come out to 90 meters when W = 13 m and L = 32 meters?
P = 2(13 m) + 2(32 m) = 26 m + 64 m = 90 m. YES.
W = 13 m; L = 32 m (answer)
The width of the rectangular garden is 13 meters and the length is 32 meters.
Explanation:The problem pertains to perimeter of a rectangle, which is calculated by the formula 2*(length + width). You're told the perimeter is 90 meters, and that the length is 6 meters longer than twice the width.
So, let's denote the width as x. Then the length would be 2x + 6.
Substitute these expressions into the perimeter formula: 2*(x + 2x + 6) = 90. Simplifying this equation gives us 6x + 12 = 90.
Subtract 12 from both sides of the equation to get 6x = 78. Finally, divide each side by 6 to solve for x, which results in x = 13.
Since x represents the width of the rectangular garden, the width is 13 meters. The length, which is twice the width plus 6, is 2*13 + 6 = 32 meters.
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The statement below describes a situation in which opposite quantities combine to make 0. Is the statement true or false? A plane takes off, circles the airport, then lands at the same airport
Answers
500 - 500 = 0
Answer:
its true
Step-by-step explanation:
Given right triangle JKM, which correctly describes the locations of the sides in relation to ∠J? a is the hypotenuse, b is adjacent, c is opposite a is the hypotenuse, b is opposite, c is adjacent a is adjacent, b is opposite, c is the hypotenuse a is opposite, b is the hypotenuse, c is adjacent
Answers
The side opposite to the right angle is the "opposite" side while the side adjacent to the right angle is the "adjacent" side. The hypotenuse of the right-angles triangle is the side opposite to the right angle.
As an example, please take a look at the attached image:
Taking a look at this image, we will find that:
both a and b are adjacent sides while c is the opposite of the right angle. c is also considered as the hypotenuse of the triangle.
Answer:
Your answer would be option A. a is the hypotenuse, b is adjacent, c is opposite
Step-by-step explanation:
Hope this helps! :)
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if (sin(()−1))p =2cos(()−1)q , show that p^2 =4q^2 (1− q^2) ?.
Answers
[tex]\sin^{-1}p=2\cos^{-1}q[/tex]
For either side to be defined, we require [tex]|p|\le1[/tex] and [tex]|q|\le1[/tex]. Under these conditions, we can take
[tex]\sin(\sin^{1}p)=\sin(2\cos^{-1}q)[/tex]
[tex]\implies p=2\sin(\cos^{-1}q)\cos(\cos^{-1}q)[/tex]
[tex]\implies p=2q\sin(\cos^{-1}q)[/tex]
[tex]\implies p=2q\sqrt{1-q^2}[/tex]
[tex]\implies p^2=4q^2(1-q^2)[/tex]
as required.
To show that p^2 = 4q^2(1-q^2), we use trigonometric identities and algebraic manipulations to prove the given equation sin((θ-1)p) = 2cos((θ-1)q). By taking the inverse sine, squaring both sides, and applying trigonometric identities, we arrive at the desired result.
Explanation:To show that p^2 = 4q^2(1-q^2), we need to start with the equation sin((θ-1)p) = 2cos((θ-1)q). We can use the trigonometric identities and algebraic manipulations to prove this equation.
Start by taking the inverse sine of both sides: (θ-1)p = sin^(-1)(2cos(θ-1)q).Next, use the identity sin^(-1)(x) = θ: (θ-1)p = sin^(-1)(2cos(θ-1)q) becomes p = sin^(-1)(2cos(θ-1)q)/(θ-1).Square both sides of the equation to eliminate the inverse sine: p^2 = (sin^(-1)(2cos(θ-1)q)/(θ-1))^2.Apply the identity sin^2(θ) = 1 - cos^2(θ) to the right side of the equation: p^2 = (1 - cos^2(sin^(-1)(2cos(θ-1)q)/(θ-1))))Finally, simplify the equation using algebraic manipulations to arrive at p^2 = 4q^2(1-q^2).Learn more about Trigonometry here:https://brainly.com/question/31896723
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the product of two consecutive integers is 272. which quadratic can be used to find x, the smaller smaller number?
Answers
x(x+1)=272
x²+x=272
x²+x-272=0
The quadratic equation that can be used to find x the smaller number is x^2 + x - 272 = 0.
What is a quadratic equation?A quadratic equation is a polynomial which has the highest degree equal to two. It is a second-degree equation of the form ax² + bx + c = 0, where a, b, are the coefficients, c is the constant term, and x is the variable.
For the given situation,
Let the integer be x and the consecutive next integer be x+1.
The product of two consecutive integers is 272,
⇒ [tex]x(x+1)=272[/tex]
⇒ [tex]x^{2} +x=272[/tex]
⇒ [tex]x^{2} +x-272=0[/tex]
Hence we can conclude that the quadratic equation that can be used to find x the smaller number is x^2 + x - 272 = 0.
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Find the improper fraction with a denominator of 12 that is equivalent to 10 1/4
Answers
30 3/12 simplify improperly to
30*12
360 +1
360/12
To find the improper fraction equivalent to 10 1/4 with a denominator of 12, convert the mixed number to an improper fraction and then multiply the numerator and denominator by a factor that will result in a denominator of 12. The improper fraction equivalent is 123/12.
Explanation:To find the improper fraction equivalent to 10 1/4 with a denominator of 12, we need to convert the mixed number to an improper fraction and then multiply the numerator and denominator by a factor that will result in a denominator of 12.
Step 1: Convert the mixed number to an improper fraction.
10 1/4 = (10 * 4 + 1) / 4 = 41/4
Step 2: Multiply the numerator and denominator by a factor that will result in a denominator of 12.
41/4 * 3/3 = 123/12
Therefore, the improper fraction equivalent to 10 1/4 with a denominator of 12 is 123/12.
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Multiply and give the answer in scientific notation: (2.3 x 10-3)(3 x 108)
Answers
=(2.3 x 3)(10^-3 x 10^8)
= 6.9 x 10^5
hope it helps
Answer:
Scientific notation of [tex](2.3\times 10^{-3})\times (3\times 10^{8})[/tex] is [tex]6.9\times 10^{5}[/tex] .
Step-by-step explanation:
As given the expression in the question be as follow .
[tex]= (2.3\times 10^{-3})\times (3\times 10^{8})[/tex]
Simplify the above terms
[tex]= 2.3\times 10^{-3}\times 3\times 10^{8}[/tex]
[tex]= 2.3\times 3\times 10^{-3}\times 10^{8}[/tex]
Now by using the exponent property
[tex]x^{a}\times x^{b} = x^{a + b}[/tex]
Thus apply this property in the above
[tex]= 6.9\times 10^{-3+8}[/tex]
[tex]= 6.9\times 10^{5}[/tex]
Therefore scientific notation of [tex](2.3\times 10^{-3})\times (3\times 10^{8})[/tex] is [tex]6.9\times 10^{5}[/tex] .