The wall is 18.79 feet high from the ground.
Data;
Length of ladder = 20ftangle of elevation = 71 degreeslength of the wall = ?Trigonometric RatioTo solve this problem, we need to use trigonometric ratio SOHCAHTOA in which we can find the missing side.
if we draw an illustration of this question, we would get
hypothenuse = 20ftangle = 71 degreesopposite = ?Using the sine angle ratio,
[tex]sin\theta=\frac{opposite}{hypothenuse}\\sin71=\frac{x}{20}\\ x=20sin71\\x=18.79ft[/tex]
The wall is 18.79ft high
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To calculate the height the ladder reaches on the wall, we use sine function and find it to be approximately 19 feet.
To find out how high up the wall the ladder touches the building when a 20-foot ladder forms an angle of 71° with the level ground, we can use trigonometry. Specifically, the sine function relates the opposite side to the hypotenuse in a right triangle. The ladder represents the hypotenuse, and the height reached on the wall is the opposite side.
Using the formula:
sin(angle) = opposite/hypotenuse
For this problem:
sin(71°) = height / 20 feet
Now we solve for height:
height = 20 feet × sin(71°)
We can calculate this using a calculator:
height ≈ 20 feet × 0.945
height ≈ 18.9 feet
To the nearest foot, the ladder reaches approximately 19 feet up the wall.
What is the value of y in the equation,
y = -3x + 4, if x = 3?
Answer:y= -5
Step-by-step explanation:
-3(3)+4= -5
-3(3)= -9
-9 + 4= -5
Answer:
-5
Step-by-step explanation:
y = -3x + 4
If x = 3
Plug the value into the expression
We have
y = -3(3) + 4
= -9 + 4
= -5
Choose the solution to this inequality.
Answer:
the answer is B
Step-by-step explanation:
you subtract 9/5 on both sides, find the common denominator which in this case would be 10. so 35-18 is 17. turn that into a mixed fraction and you get 1 and 7/10
Find the area of the rectangle that has the vertices (-2, 0). (0-4). (2.0), and (0,4), respectively.
Final answer:
Area of the rectangle that has the vertices (-2, 0). (0-4). (2.0), and (0,4) is 32 square units.
Explanation:
To find the area of a rectangle, we need to use the formula:
Area = length x width
In this case, the vertices of the rectangle are (-2, 0), (0, -4), (2, 0), and (0, 4). We can calculate the length and width by finding the difference in the x-coordinates and y-coordinates, respectively.
The length is 2 - (-2) = 4 and the width is 4 - (-4) = 8.
Therefore, the area of the rectangle is:
Area = 4 x 8 = 32 square units.
What customary unit would you use to estimate? A car is about 15 _____ long. inches meters yards feet
Answer:
feet
Step-by-step explanation:
what’s the formula? i don’t understand and i need help
Step-by-step explanation:
y+4= 4(x-3)
y+4 =4x- 12
4x-12 -y -4=0
4x-y -16=0
4x-y=16
The manager of a grocery store estimates that 74% of customers will make a purchase.
Part A: How many customers should a cashier expect until he finds a customer that makes a purchase?
Part B: What is the probability that a cashier helps 3 customers until he finds the first person to make a purchase?
Answer:
A : Per 100 people, cashier should expect 26 customer until he finds a costumer that makes a purchase.
B: The probability is 1/4
Step-by-step explanation:
The estimated chance of a customer making a purchase = 74%
So, if a TOTAL of 100 people visit the grocery store on any random day,
then 74 % of customers
= 74% of 100
= 74 people will make purchases.
⇒ Out of total 100 people visiting, 74 people will make a purchase.
So, the number of people NOT making a purchase = 100 - 74 = 26
⇒ Out of total 100 people visiting, 26 people will NOT make a purchase.
Also, 26 = 26% of 100
Part A :
So, in order to make a purchase, cashier should expect 26% of customers because the percentage of NOT purchasing is 26%.
Hence, per 100 people, cashier should expect 26 customer until he finds a costumer that makes a purchase.
Part B :
The percentage of customer making a purchase = 74%
The percentage of people NOT making a purchase = 26%
So, for every 3 customer making a purchase there is a 1 person NOT making a purchase.
So, the probability is 1/4
Part A)
1.35 customers until the cashier should expect to find a customer that makes a purchase.
1 ➗ 0.74 = 1.35
Part B)
0.013 is the probability that the cashier helps 3 customers until he finds the first person to make a purchase.
(1 - 0.74)3 x 0.74 = 0.013
Angle ABD measures (4x + 10)o. Angle ACD measures (5x − 2)o.
Circle E is shown. Angles A B D and A C D intercepts arc A D. Angles B A C and B D C intercepts arc B C.
What is the measure of arc AD?
Answer: 116°
Step-by-step explanation:
The measure of arc AD is 116 degrees and it can be determined by using the properties of a circle.
Given that,
Angle ABD measures (4x + 10).
Angle ACD measures (5x − 2).
Circle E is shown.
Angles ABD and ACD intercept arc AD.
Angles BAC and BDC intercept arc BC.
We have to determine,
What is the measure of arc AD?
According to the question,
Angle ABD measures (4x + 10).
Angle ACD measures (5x − 2).
Circle E is shown.
Angles ABD and ACD intercept arc AD.
Angles BAC and BDC intercept arc BC.
In the given condition, Angle ABD and Angle ACD have inscribed angles, intercepting the same arc then by the intercept arc property.
Angle ABD = Angle ACD
[tex]\rm 4x+10 = 5x-2\\\\4x-5x = -2-10\\\\-x = -12\\\\x=12[/tex]
The value of x is 12.
Therefore,
The measure of arc AD is,
[tex]\rm Arc \ AD =A ngle \ ABD + Angle \ ACD\\\\Arc \ AD = (4x+10) + (5x-2)[/tex]
Substitute the value of x,
[tex]\rm Arc \ AD = (4x+10) + (5x-2)\\\\Arc \ AD = 4(12) +10+5(12) -2\\\\Arc \ AD = 48+10+60-2\\\\Arc \ AD = 116 \ degree[/tex]
Hence, the measure of arc AD is 116 degrees.
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How do you model 18 more than 27 on the number line?
Answer:
You count 18 places to the right of 27.
Step-by-step explanation:
To the right of a point, the numbers are increasing, therefore you have to go to the right 18 of 27.
The modeling 18 more than 27 on the number line should be explained below.
Number line:A line on which numbers are mentioned at intervals and the same is considered for doing simple numerical operations. Here we have to count 18 places to the right of 27. In this, the positive number, as well as the negative numbers, are mentioned. It could be in any kind of direction, mainly it should be in the horizontal direction.
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What is true about triangle AMB?
It is congruent to triangle ABC.
It is an obtuse triangle.
It is an isosceles right triangle.
It is a scalene triangle.
Answer:option c
Step-by-step explanation:
An Isosceles Right Triangle is a right triangle that consists of two equal-length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
So the correct answer is option c. It is an isosceles right triangle.
What are the sides of an isosceles right triangle?
Since the two sides are equal it makes the corresponding angle congruent. Thus, in an isosceles right triangle two sides are congruent and the corresponding angles will be 45 degree each which sums to 90 degree. So the sum of three angles of the triangle will be 180 degrees.
What is the formula for an isosceles right triangle?
The area of the isosceles right triangle follows the general formula of the area of a triangle that is (1/2) × Base × Height. In ∆QPR shown above with side lengths PQ = QR = x where PQ represents the height and QR represents the base, the area of isosceles right triangle formula is given by 1/2 × PQ × QR = x2/2 square units.
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Simplify the numerical expession 5-2 + 12 + 4?
Answer:
The answer is 19
Step-by-step explanation:
Answer:so easy its 19 it's right i promise you
Bobby catches 8 passes in 3 football games. At this rate, how many passes does he
catch in 15 games?
Answer:
40 passes
Step-by-step explanation:
we know that
Bobby catches 8 passes in 3 football games
so
using proportion
Find out how many passes does he catch in 15 games
[tex]\frac{8}{3}=\frac{x}{15}\\\\x=8(15)/3\\\\x=40\ passes[/tex]
Answer: 40 passes
Step-by-step explanation:
Hi, to answer this we have to use proportions:
Proportion = Passes catched/ football games
Bobby catches 8 passes in 3 football games: 8/3
For 15 games: x/15
8 /3 = x/15
Solving for x
(8/3)15 =x
40 = x
He catches 40 passes in 15 games.
Feel free to ask for more if needed or if you did not understand something.
The distance of one lap around a school track is 1/4 miles. Karen walks 6 laps around the track and realizes it is in
poor condition. She complains and asks to see the manager of the track.
How many more laps must Karen walk to reach a total distance of 5.5 miles?
laps
Answer:
16
Step-by-step explanation:
because 5.5 is 22 laps and you do 22-6=16.
$750 is invested at 11% compounded quarterly. how much is the account after 10 years?
Answer:
F= $2219.91
Step-by-step explanation:
[tex]F=P(1+i)^{n}[/tex]
Here
F= value of money after 10 years
P= present value
i= interest
n= number of compound on money
P=$750 i = 11%/4=0.0275 n=10x4= 40
[tex]F=750(1+0.0275)^{40}[/tex]
[tex]F=750(1.0275)^{40}[/tex]
[tex]F=750(2.96)[/tex]
F= $2219.91
What is the answer to 50% of $36
Answer:
$18
Step-by-step explanation:
1/2*36=18
Therefore, $18
Answer:$18
Step-by-step explanation:
50% of 36
50/100 x 36
1/2 x 36=36/2=18
The probability that a softball player named Casey gets a base hot during a single time at bat is 4/10. If he goes to bat 4 times in his next game (which is played in Mudville), determine:
A)The probability that he gets 4 hits.
B) the probability that he gets no hits, causing no joy in Mudville.
C) the probability that he gets 3 or more hits.
Final answer:
To determine the probabilities of Casey's performance in a softball game, we compute the outcomes of him getting 4 hits (0.0256), getting no hits (0.1296), and getting 3 or more hits (0.2048) using the rules of probability for independent events.
Explanation:
The probability of the softball player Casey getting a hit is 4/10. To solve the various probabilities related to Casey's performance:
A) The probability that he gets 4 hits in 4 at-bats can be calculated by raising the probability of getting a hit to the fourth power since each at-bat is an independent event. This gives us (4/10) 4 or 0.0256.B) The probability that he gets no hits in 4 at-bats is the probability of not getting a hit (which is 1 - 4/10 = 6/10) raised to the fourth power, resulting in (6/10) 4 or 0.1296.C) The probability that he gets 3 or more hits is the sum of the probabilities of getting exactly 3 hits and getting 4 hits. To get exactly 3 hits, we can calculate 4 choose 3 (which is 4) times the probability of getting a hit three times and not getting a hit once, giving us 4 * (4/10) 3 * (6/10). Adding the probability of getting 4 hits, we get 0.1792 + 0.0256 = 0.2048.Concrete Works manufactures and sells cement trucks. For the previous year, their taxable income was $6,775,989.00. They have
to pay a federal tax rate of 35%, a state tax rate of 8%, and a local tax rate of 2%. As part of their loan package for the business, the
company has to pay $3,200,000.00 after the taxes are paid each year to go against the principal amount of the loan. The profit after
taxes and principal reduction can be determined by the equation
p() = 0.586041 - 3,200,000,
where x is their taxable income. How much profit does the company have after paying taxes and reducing the principal on the loan?
You have the right equation.
p(x) = 0.586041x - 3,200,000
3200000 of course represents the deduction from the loan
0.586041 - this number represents the amount of money left after taxes (58.6041% of the total is left)
We get this by taking into account all the taxes on top of another...
35% federal tax = 65% left
35% federal tax and 8% state tax = 65% x 92% left
35% federal tax and 8% state tax and 2% local tax = 65% x 92% x 98% left = 58.6041%
To get the profit plug in the given taxable income for x.
p(6775989) = 0.586041(6775989) - 3,200,000 = $771,007.37 approx.
answer: $771,007.37 approx.
2x - y = 10
y = -x - 1
Solve the system of equations
A (9.8)
B (3.-4)
C no solution
Answer: option is C
Step-by-step explanation:
What will be the new position of the given point (-6,8) after rotating 90° clockwise about the origin
Answer:( 8, 6)
Step-by-step explanation:
After rotating the point (-6,8) 90° clockwise about the origin, the new position of the point will be (8,6).
Explanation:When a point is rotated 90° clockwise about the origin in a two-dimensional Cartesian coordinate system, the new position of the point can be calculated by changing the sign on the y-coordinate and swapping the order of the x and y-coordinates. For your specific question, we are given the point (-6,8). So, the new position of the point after the rotation would be (8,6). This is because rotations in a clockwise direction can be considered as negative in mathematics, and portions rotate around the origin following the right-hand rule.
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Answer this question in this image below, please anyone
The height of the cone is 4 inches.
Step-by-step explanation:
Step 1:
The given triangle is a right-angled triangle.
The length of the hypotenuse is 5 inches. One of the other sides is 3 inches long. Assume the other side of the triangle measures x inches.
According to Pythagoras' theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Step 2:
(The length of the hypotenuse)² = (The other sides length)² + (The other sides length)²
By substituting the values in the equation, we get
[tex]5^{2} = 3^{2} + x^{2} , x^{2} = 25 - 9 = 16.[/tex]
[tex]x = 4.[/tex]
So the height of the cone is 4 inches which is the fourth option.
(7+x)+7x simplify each expression
Step-by-step explanation:
[tex](7 + x) + 7x \\ = 7 + x + 7x \\ = 7 + (x + 7x) \\ = 7 + 8x \\ = 8x + 7[/tex]
Cindy rode her bicycle 6 miles less than four times the number of miles that Scotty road. If Cindy rode his bicycle 42 miles, how many miles did Scotty ride?
Answer:
12
Step-by-step explanation:
42+6=48
48/4=12
You are writing the inequality for age. At an amusement park, children ages 3 and under are free. Write an inequality.
Answer:
Step-by-step explanation:
So you would do x as other ages, 3 as well obviously 3.
x < 3
THE < WILL HAVE A LINE UNDER IT!
The line stands for less than or EQUAL to. In this case, you have to be 3 or younger. Do not forget the line under the <. I am unable to type it!
The question is about writing an inequality to represent the ages of children who can enter an amusement park for free. The correct mathematical expression according to the given scenario is 'age ≤ 3'.
Explanation:The subject of the question deals with the practical application of inequalities in a real-world context. In this case, the inequality would represent the ages at which children could enter an amusement park for free. According to the amusement park policy, children ages 3 and under are free. In mathematical terms, this can be expressed as 'age ≤ 3'. The symbol '≤' represents 'less than or equal to', indicating that the age could be any number less than or equal to 3.
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An online video game club charges $10 to join and $8 per month after that. Which equation can you solve to find out how long you can be a member for $75 An online video game club charges $10 to join and $8 per month after that. Which equation can you solve to find out how long you can be a member for $75
Is 9,056,198 divisible by 5?
Answer:
No, because the end of the number is 8 and numbers divisible by 5 has to end in 0 or 5.
HOPE THIS HELPED!Answer:
No
Step-by-step explanation:
9,056,198 is not divisible by 5.
Being divisible means that the number can be divided by the other without there being any decimals. Meaning it has to divide into a whole number in order to be divisible.
An easy way to see if anything is divisible by 5 is to see if the last number is either a 0 (for example 10 or 20) or if the last number is a five (for example 15 or 25)
which ordered pair is a a solution of the equation ?
y= 3x+5
A. only (2,11)
B. only (3,13)
C. both (2,11) and (3,13)
D.neither
Answer:
A
Step-by-step explanation:
when you plug in 2,11
11 = 3*2 +5 that is correct
13 = 3*3 +5 that is not correct
only 2,11 works
Answer:
A. only (2,11)
Step-by-step explanation:
Apples weigh 12 ounces each.Ronald bought 4 apples.How many pounds of apples did he buy?
+32. Convert 45°F to
The formula to convert Celsius to Fahrenheit is F
Celsius. Round to the nearest degree.
O A. 49°C
O B. 113°C
O C. -1°C
O D. 7°C
Answer:
Option D. 7°C
Step-by-step explanation:
Let the temperature in Fahrenheit (F) and the temperature in Celsius(C)
The formula to convert Fahrenheit to Celsius is ⇒ F = 1.8 C + 32
So, to Convert 45° F to Celsius, substitute with with 45° F
45 = 1.8 C + 32
Solve for C
1.8 C = 45 - 32
1.8 C = 13
C = 13/1.8 = 7.222
Rounding to the nearest degree ⇒ 45° F = 7° C
The answer is option D. 7°C
3x^2(2x^2+3)=0
please help quick
Answer:
x=0 and x=sqrt(3/2)i
Step-by-step explanation:
3x^2(2x^2+3)=0
Make into two equations due to Zero Product Property:
3x^2=0 and 2x^2+3=0
x^2=0 2x^2=-3
x=0 x^2=-3/2
x=sqrt(3/2)i
a plane ticket barcelona costs £175 the price decreases by 6% work out the new price
Answer: £164.50
175 decreased by 6% = 164.5
Absolute change (actual difference):
164.5 - 175 = - 10.5
Step-by-step explanation:
175 - Percentage decrease =
175 - (6% × 175) =
175 - 6% × 175 =
(1 - 6%) × 175 =
(100% - 6%) × 175 =
94% × 175 =
94 ÷ 100 × 175 =
94 × 175 ÷ 100 =
16,450 ÷ 100 =
164.5
£164.50
Answer: £164.5
Step-by-step explanation:
Given ticket cost at = £175
6 percent decrease = 6/100 × £175
=£10.5
To get the Current cost of ticket, we then subtract 6% decrease from the former cost of ticket:
= £175 - £10.5
=£164.5
I hope this helps.
Which expression has the same value as 3 ÷ 5/9?
A. 3 × 5/9
B. 13 ÷ 5/9
C. 3 ÷ 9/5
D. 3 × 9/5
Answer:
D. 3 x 9/5
Step-by-step explanation:
The expression that has the same value as 3 ÷ 5/9 is 13 ÷ 5/9.
Explanation:The expression that has the same value as 3 ÷ 5/9 is option B. 13 ÷ 5/9.
To divide by a fraction, we multiply by its reciprocal. In this case, we can find the reciprocal of 5/9, which is 9/5. So, we have 3 ÷ 5/9 = 3 × 9/5 = 27/5.
Option B, 13 ÷ 5/9, is equivalent to 13 × 9/5 = 117/5, which is equal to 27/5. Therefore, option B has the same value as 3 ÷ 5/9.
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