Answer: To find the height of the flagpole, we can use the fact that the angles of depression and elevation are complementary angles, meaning that they add up to 90°.
Let's call the height of the flagpole "h". Then, we have:
h - 6 = h * tan(4°) (the height difference between Javier and the bottom of the flagpole)
and
h = 6 + h * tan(25°) (the height of the top of the flagpole as seen by Javier).
By substituting the first equation into the second, we can find h:
h = 6 + h * tan(25°)
h = 6 + h / tan(65°)
h * tan(65°) = 6 + h
h * tan(65°) - h = 6
h = 6 / (tan(65°) - 1)
Using a calculator, we find that h = approximately 43.3 feet. Rounding to the nearest foot, the height of the flagpole is 43 feet.
Step-by-step explanation:
x^2+y^2=100 is it a function?
The equation x^2+y^2=100 is not a function
How to determine if it is a functionFrom the question, we have the following parameters that can be used in our computation:
x^2 + y^2 = 100
The above equation is a circle equation
As a general rule, we have
Circle equations are not functions and they do not represent a function on a graph
Hence, x^2+y^2=100 is not a function
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what is c over 2 < -0.75=
The value of c lies in the interval [tex](-\infty, -1.5)[/tex]
What is inequality?Inequality is a statement that shows the relationships the two expressions are not equal. It is defined by the symbols like <, >, ≤, ≥.
[tex]\frac{c}{2} < -0.75[/tex]
To find the value of c:
[tex]\frac{c}{2} < -0.75[/tex]
Multiply both sides by 2 we get,
[tex]2\frac{c}{2} < (-0.75)*2[/tex]
⇒c < -1.5
Therefore c<-1.5 is the solution for the given inequality.
It can also be represented in the interval form.
This is given in the interval notation [tex](-\infty, -1.5)[/tex]
Hence, the value of c lies in the interval [tex](-\infty, -1.5)[/tex]
Complete question:
What is the values that c can take when [tex]\frac{c}{2} < (-0.75)[/tex]?
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Need help, please, thanks!
The earnings in the simple interest and compound interest for a 5 year period is in the table below where S is for Suzanne and D is for Derrick
S - annual interest S - Balance D - annual interest D - Balance
Year 1 147 3147 147 3147
Year 2 294 3294 301.2 3301.2
Year 3 441 3441 462.96 3462.96
Year 4 588 3588 632.65 3632.65
Year 5 735 3735 810.65 3810.65
How to solve simple interestSimple interest is calculated by the formula
principal x time x rate / 100
In the problem
Principal = $3000
rate = 4.9%
time is varying from 1 to 5
For the first year we have
= 3000 * 1 * 4.9 / 100
= 147
Compound interest the formula is
Principal(1 + rate)^(year) - 1)
For the first year, (the rate is already divided by 100 to get 0.049) we have
= 3000(1 + 0.049)^(1) - 1)
= 147
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From the top of a 450-foot cliff, a hiker looks down at a river below. Her angle of
depression to the near and far banks of the river are 80° and 50° respectively, as
shown in the picture. Based on this information, how wide is the river?
The width of the river is calculated by the tangent of the angle will be 293 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Observing a river below from the top of a 450-foot cliff, a hiker. Her depression lies at an angle of 80° to the near bank and 50° to the far bank of the river.
The horizontal distance when the angle is 80° is given as,
tan 80° = 450 / x₁
x₁ = 84.64 feet
The horizontal distance when the angle is 50° is given as,
tan 50° = 450 / x₂
x₂ = 377.59 feet
The width of the river is given as,
W = x₂ - x₁
W = 377.59 - 84.64
W = 292.95
W ≈ 293 feet
The width of the river is calculated by the tangent of the angle will be 293 feet.
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A cylinder-shaped scoop has a base radius of 2 centimeters and a height of 5 centimeters. The scoop has a mass of 14.9 grams when empty. The scoop is completely filled with water. One cubic centimeter of water has a mass of one gram. What is the mass of the scoop of water in grams, including the mass of the scoop? Describe how you found your answer. Round to the nearest tenth.
Answer:
77.7 g
Step-by-step explanation:
You want the mass of a cylindrical scoop of radius 2 cm and height 5 cm when it is filled with water at 1 g/cm³, and has an empty mass of 14.9 g.
WaterThe mass of the water will be the product of its volume and its density. The volume is that of a cylinder with radius 2 cm and height 5 cm. That volume is given by the formula ...
V = πr²h = π(2 cm)²(5 cm) ≈ 62.83 cm³
The mass of the water is then ...
(62.83 cm³) × (1 g/cm³) = 62.83 g
Total massThe total mass of the water-filled scoop is the sum of its empty mass and the mass of the water:
scoop + water = 14.9 g + 62.8 g = 77.7 g
The mass of the scoop and water is 77.7 grams.
PLEASE ANSWER ASAP THANKS
The value of x is 97.
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
From the figure,
(x - 5) and (x - 9) forms a straight angle.
This means,
x - 5 + x - 9 = 180
Solve for x.
2x - 14 = 180
2x = 180 + 14
2x = 194
x = 97
Thus,
The value of x is 97.
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The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 18 45 72
White 13 B 65 C
Determine which table has the correct values for A, B, and C.
Black 8 18 45 72
White 13 25 65 105
Black 9 18 45 72
White 13 26 65 104
Black 9 18 45 72
White 13 39 65 117
Black 1 18 45 72
White 13 26 65 104
Using the given ratios found the values of A, B and C, and completed the table as follows:
Black 9 18 45 72
White 13 26 65 104
What is meant by the ratio?
A ratio in mathematics demonstrates how many times one number is present in another. A ratio is what a fraction looks like when it is written as a:b. A ratio is the comparative or condensed version of two quantities of the same type.
Given the table:
Black A 18 45 72
White 13 B 65 C
The table represents the ratios of black keys to white keys on pianos of various sizes.
The ratio of keys of the piano always remains constant.
So we can write as follows:
A/13 = 18/B = 45/65 = 72/C
To find A, we take the following ratios.
A/13 = 45/65
On solving, we get
A = 45 * 13 / 65 = 585/65 = 9
To find B, we take the following ratios.
18/B = 45/65
B = 18 * 65 / 45 = 1170/45 = 26
To find C, we take the following ratios.
72/C = 45/65
C = 72 * 65 / 45 = 104
Therefore using the given ratios we can complete the table using the values of A, B and C,
Black 9 18 45 72
White 13 26 65 104
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You must spend at least $10 at the grocery store to get a free greeting card
Answer:
I spent 13.32 at the store the other day...?
Step-by-step explanation:
What is the question.
Penny is vacationing at the beach and decides to purchase a pair of swim goggles and a
sand bucket which she randomly selects off the shelf. When she realizes that they are
both green, she states that "because she selected a green pair of swim goggles, she was
more likely to select a green sand bucket." Do you agree or disagree with Penny's
statement? Justify your thinking
Answer: I disagree with Penny's statement. The probability of her selecting a green pair of swim goggles and then a green sand bucket is the product of their individual probabilities. The fact that she selected a green pair of swim goggles does not change the probability of selecting a green sand bucket. Each selection is independent of the other, and the probabilities of each event remain the same. So, Penny's statement that "because she selected a green pair of swim goggles, she was more likely to select a green sand bucket" is not valid.
Step-by-step explanation:
HELP PLSS I NEED HELPPPPP
The required measures of length are, as follows:
GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.
What is a rectangle?A rectangle is defined as a four-sided shape with opposite sides that are equal in length and parallel to each other.
The lengths are given in the question, as follows:
DE = 11
GH = 14
Since DE and GF are opposite sides then both are equal.
So GF = 11
Here GH and HF are equal,
HF = 14
∵ GE = GH + HE = 14 + 14 = 28
As we know that the two lengths of the diagonals are equal in the rectangle.
So GE = DF
So DF = 28
Using the Pythagorean theorem, we have
DG² + GF² = DF²
DG² + 11² = 28²
DG² + 121 = 784
DG² = 663
DG = 25.75
Thus, the measures are, as follows:
GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.
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Raul is wrapping a cylindrical package with wrapping paper. He has two different packages to choose from:
Package A has a radius of 1.5 inches and a height of 6 inches
Package B has radius of 2 inches and a height of 3 inches
He has 70 in2 of wrapping paper and he will need to cover all sides of the package.
Using the formula SA = 2π
rh + 2π
r2, determine which of the following packages Raul will have enough wrapping paper to cover.
Package A has a surface area of
Choose...
in2. Package B has a surface area of
Choose...
in2.
Raul will have enough paper to wrap
Choose...
The package that will have enough wrapping paper to cover is package B
Package A has a surface area of 70. 65 in²
Package B has a surface area of 62. 8 in²
How to determine the surface areaThe formula for the surface area of a cylinder is expressed as;
SA = 2πrh + 2π
Given that the parameters are;
r is the radiush is the height of the cylinderFor Package A, substitute the values
= 2 × 3.14 × 1.5 × 6 + 2 × 3.14 × (1.5)²
Multiply the values, we have;
= 70. 65 in²
For package B, substitute the values, we get;
= 2 × 3.14 × 2 × 3 + 2× 3.14 × (2)²
Multiply the values
= 62. 8 in²
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can someone explain the questions attached? thanks
The probability of landing on the head side of coin and rolling a 3 on the die is found as 1/12.
Explain about the term sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of feasible experiment results. Depending on the experiment, a sample area could contain a variety of results.Sample space for tossing a coin: (H,T)
P(head) = 1/2
Sample space for tossing a dice : (1, 2, 3, 4, 5, 6)
P(3) = 1/6
So,
Probability of head with 3 on the die = 1/ 2* 1/6 = 1/ 12
Thus, the probability of landing on the head side of the coin and rolling a 3 on the die is found as 1/12.
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The correct question is-
A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.
Enter your answer as a fraction in the form a/b (for example 2/3, 5/7) or as an integer.
1. Arturo earns n dollars per hour. Next month
he will receive a 2% raise in pay per hour. The
expression n +0.02n is one way to represent
Arturo's pay per hour after the raise. Write
an equivalent simplified expression that will
represent his pay per hour after the raise.
The equivalent simplified expression is 1.02n.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Given that, Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour.
The expression n +0.02n is one way to represent Arturo's pay per hour after the raise.
Here, the equivalent expression is n +0.02n= 1.02n
Therefore, the equivalent simplified expression is 1.02n.
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What is X and Z. please tell me
x = 5
z = 118°
Step-by-step explanation:
opposite angles are equal
(6x + 32)° = 62°
6x = 62° - 32°
6x = 30°
x = 5°
angles on a straight line add up to 180
180° = 62° + z
z = 180° - 62°
z = 118°
solve
(2x-3) (x2+4x-5)
Answer: 2x^3 + 5x^2 - 10x + 15
Step-by-step explanation:
To multiply two polynomials, you can use the distributive property and multiply each term of one polynomial by each term of the other. In this case, the two polynomials are (2x - 3) and (x^2 + 4x - 5), so we have:
(2x - 3) * (x^2 + 4x - 5) =
2x * x^2 + 2x * 4x - 2x * 5 +(-3) * x^2 + (-3) * 4x - (-3) * 5
Expanding the products, we get:
2x^3 + 8x^2 - 10x - 3x^2 - 12x + 15
Combining like terms, we get: 2x^3 + 5x^2 - 10x + 15
PLEASE HELP 25 POINTS!! NO LINKS
Answer:
C i think
Step-by-step explanation:
Convert 2 pints into milliliters. Round your answer to the nearest whole number.
Answer: 946 ml
Step-by-step explanation: 1 pint= 473.2
2*
473.2= 946.4
=946 ml
8 A crystal paperweight
is shaped like a cylinder with a star-shaped hole. The
top of the star-shaped hole is shaped like a square with four points that are
identical equilateral triangles. The height of the cylinder is 3 centimeters. Find
the volume of the paperweight.
Please Help ASAP!!!
The volume of the paperweight is 79.3 cm³.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
From the given information, The area of the star-shaped cutout is,
A square has a side length of 2 cm, and four equilateral triangles have a side and a height of 2 cm.
So, The area of the star-shaped cutout is,
= (2×2) + 4×(1/2)×2×2.
= 4 + 8.
= 12 cm.
Now, The volume of the star-shaped cut-out is,
= 12×height,
= 12×3.
= 36 cm³.
And the volume of the cylinder is,
= π(1 + 2 + 0.5)²×3.
= π(3.5)²×3.
= 115.4 cm³
Therefore, The volume of the paperweight is,
= 115.4 - 36 cm³.
= 79.3 cm³.
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Simplify the following by rationalizing the denominator. need rightnow pahelp.
Answer:
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
Exact Form:
3√2+2
7
Decimal Form:
0.89180581
…
a || b and p is a transversal. If m 1 = 140°, find the
measure of each angle giving one reason for each answer.
(The first one is done for you.)
Answer:
Angle 4 = 140
Angle 3= 40
Angle 5=140
angle 6=40
angle 7=40
Step-by-step explanation:
Adjacent angles are congruent. Thats how I can tell angle 4 is 140. And also how i can tell angle 3 is 40. Any questions?
im not explaining the rest im too tired
btw I also do 8th math lol it stinks.
Two important ingredients for baking bread are
yeast and flour. To make a loaf of bread of at
most
30 servings, maintain a yeast to
flour ratio of 1:200. If you're making a loaf of more than 30
servings, use a ratio of 1:180.
If you're making 30 servings
of bread and using 0.25 oz of yeast, how many ounces of flour do you
need?
If you're making 60 servings of bread and using 540 oz of flour, how many ounces of yeast do you
need?
NOTE: Enter only numerals for each of your answers.
If you're making 60 servings of bread and using 540 oz of flour, then the number of ounces of yeast you need is 3 oz.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, to make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200. If you're making a loaf of more than 30 servings, use a ratio of 1:180.
If you're making 30 servings of bread and using 0.25 oz of yeast, then
0.25/Flour = 1/200
Flour = 50 oz
If you're making 60 servings of bread and using 540 oz of flour, then
Yeast/540 = 1/180
Yeast = 3 oz
Therefore, if you're making 30 servings of bread and using 0.25 oz of yeast, then the number of ounces of flour you need is 50 oz.
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What is the degree of 7c3d2
The degree of the expression 7c³d² is 2
How to determine the degreeFrom the question, we have the following parameters that can be used in our computation:
Expression = 7c³d²
The degree of an expression is the highest power in the expression
In this case,
7c³ = Constant
d² = Variable
The highest power of the variable is 2
Hence, the degree is 2
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-3x² + 2x-5 = y
-x+2=-y
Answer: \left(h,\:k\right)=\left(\frac{1}{3},\:\frac{14}{3}\right),\:p=\frac{1}{12\
Step-by-step explanation:
A car is bought for £8500
In it's first year it's price reduces by 10%
Each year after that it decreases by 5%
What is the price after 3 years?
Answer: The price after 3 years is £6904.15
Step-by-step explanation:
After 1 year, 8500*0.9= 7650
7650*0.95=7267.5
7267.5*0.95=6904.125
The price after 3 years is £6904.15
[tex]1\frac{1}{3} :2\frac{1}{3}[/tex]
Answer:
Given: [tex]1\frac{1}{3} :2\frac{1}{3}[/tex]
To simplify this ratio, convert the mixed fractions into improper fractions:
[tex]\frac{4}{3}[/tex] : [tex]\frac{7}{3}[/tex]
Then to divide ( because ratio = division ) turn around [tex]\frac{7}{3}[/tex] and multiply:
[tex]\frac{4}{3} * \frac{3}{7}[/tex]
Then multiply:
[tex]\frac{12}{21}[/tex]
Finally simplify this fraction by dividing the denominator & numerator by 3:
= [tex]\frac{4}{7}[/tex]
...
Solve for x . circles tangent 1 A. 12 B. 10 C. 42 D. 9
8 is the measure if the angle x in the given diagram.
Circle geometryThe point where two lines meet is known as an angle. The given diagram is a circle geometry.
Using the theorem, angle at the arc is twice the angle at the vertex, we will have:
80 = 2(4x + 8)
80/2 = 8x + 8
40 = 4x + 8
4x = 40 - 8
4x = 32
x = 32/4
x = 8
Hence the value of x from the diagram given is 8
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An online app charges $0.99 to download a song and $7.99 membership fee. (A)Write an expression that gives the total cost in dollars to download “s” songs. (B)Then, find the cost of downloading 12 songs. Incorrect work/solutionCorrect work/solution (A) s(0.99 + 7.99) = 0.99s + 7.99s = 8.98s = (B) 8.98(12) = 8.98 x 12 = $107.76 for 12 songs Part A:Explain what this student did incorrectly.
Answer: The student correctly wrote an expression to find the total cost of downloading "s" songs. The expression is: 0.99s + 7.99. However, they made a mistake when they simplified the expression to 8.98s. The expression should have remained as 0.99s + 7.99, because the $7.99 membership fee does not change regardless of how many songs are downloaded.
In Part B, the student correctly used the expression to find the cost of downloading 12 songs. They multiplied 8.98 by 12 and got the correct answer of 107.76.
Step-by-step explanation:
If you take - 3/10 of a number and add 1, you get 10. Write an equation to represent the situation. What is the original number
Answer: -30
Let's call the original number "x". Then, we can write the equation as follows:
-3/10 x + 1 = 10
To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:
-3/10 x = 9
x = (9 * 10)/(-3)
x = -30
So, the original number is -30.
Suppose that n 0 and n 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P (x) y = Q(x) y^n into the linear equation dy/dx +(1-n)p(x)v(x)=(1-n)q(x).
The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:
The equation is in the form
dy/dx +P(x)y=Q(x)yⁿ, where P and Q are functions of x or constants, this is called Bernoulli's equation.
Now, we have to substitution using
[tex]v = {y}^{1 - n} [/tex]
Differentiating both side with respect to 'x'
[tex]v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'[/tex]
we get,
[tex]= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)[/tex]
Now, by using
[tex]v' = {y}^{1 - n} [/tex]
The given equation is expressed as:
[tex]v + (1 - n)p(x)v = (1 - n)q(x)[/tex]
or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)
The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.
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One way to establish validity of a questionnaire is my measuring:A) The correlation between the score on the questionnaire and another measure of the same conceptB) The alpha value of the reliability coefficientC) How well sunjects perform on the questionnaire at one time compared to another timeD) The consistency by which multiple sunjects are able to complete the questionnaire without error
The correct option is Option D) The consistency with which several individuals can complete the questionnaire without making an error is one technique to determine a questionnaire validity.
A questionnaire is a sort of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a collection of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Despite the fact that surveys are frequently created so that the answers may be statistically analyzed. Consequently, it may not be practical to conduct a survey using a questionnaire for some demographic groups.
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