Answer:
C. the use of a series of numbers in which each number is an equal distance from the next.
Step-by-step explanation:
The four characteristics of mapping rules are:
1. Classification: This is the grouping of data or information based on given criteria.
2. Order: this is the chronological arrangements of numbers.
3. DISTANCE: This is the range or difference between one unit to the other.
4. Origin
A baseball fan is seated in the upper deck of a stadium 200 feet away from
homeplate. If the angle of depression to the field is 62 degrees, at what height is
the fan sitting? Hint: draw a picture and label the parts of the triangle and use
your trig ratio to find the height.*
Please find attached to this answer a well labelled diagram of the triangle
Answer:
Approximately 176.6 feet
Step-by-step explanation:
From the question, we are to find the height at which the baseball fan was sitting.
From the attached diagram the height at which the fan was sitting is equivalent to the opposite side of the triangle.
Hence , the appropriate trigonometric function to use to solve this question is the sine function.
Sine = Opposite / Hypotenuse
Opposite is unknown so we refer to it as Y
Hypotenuse = 200feet
While the Angle of depression = 62°
Therefore,
Sine 62° = Y/ 200 feet
Cross multiply
Sine 62° × 200 feet = Y
Y = 176.58951857 feet
Approximately 176.6 feet
Therefore , the height at which the fan is sitting is 176.6 feet
Mike discovered that the pool in his backyard is leaking slowly. The pool holds 18,968 gallons of water, and is leaking at a rate of 12 gallons per day. If mike does not replace the water that has leaked from the pool, how many gallons of water will remain in the pool after 68 days?
Answer:
18,152 Gallons
Step-by-step explanation:
First, you'll want to put this into an equation. We'll use x as the amount of water in gallons that will remain in the pool.
18,968 - 12 (68) = x
First, we'll multiply - 12 and 68.
We'd end up with this:
18,968 - 816 = x
From here, we can just subtract 816 from 18,968.
18,152 = x
Now we can see that there will be 18,152 gallons of water left in the pool after 68 days.
What is the value of this expression when x = negative 1 and y = 2?
4 x cubed y squared
Answer:
the correct answer is -16
Step-by-step explanation:
I took the test
The solution for the expression 4x³y² at x = -1 and y =2 will be -16.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the expression is 4x³y². The values of x and y are -1 and 2.
The expression at the values of x and y will be solved as:-
E = 4x³y²
Substitute the values of x = -1 and y = 2.
E = 4x³y²
E = 4 x ( -1)³ x ( 2 )²
E = 4 x -1 x 4
E = -16
The value of the expression at x =-2 and y = 2 will be -16.
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write an equation for the function that includes the following points (2, 32) and (3, 64)
Answer:
y=32x-32
Step-by-step explanation:
this time no algorithm or equation was needed i saw that if the equation was y=32x there would be ordered pairs (1,32) and (2,64) so to delay it by 1 on the x side just subtract the slope from the y - intercept sorry if that doesn't make sense
What are the answers
Answer:
x = 1, y = 1
Step-by-step explanation:
Use system of equations to solve for x and y by using substitution
The solution to the system of equations, though we can solve using substitution, can also be found by graphing these equations. If you graph these equations, look for where they intersect (it should be one point!).
-5x + 6 = 3x - 2
6 = 8x - 2
8x = 8
x = 1
y = 3(1) - 2
y = 3 - 2
y = 1
Hope this helps!! :)
Jenna has 30 buttons. She is organizing her buttons into 6 boxes. She puts the same number of buttons in each box. Write an expression that you use to find the number of buttons in each box.
Answer:
The expression will be x = 30/6 and she'll have 5 buttons in each box.
Step-by-step explanation:
In order to write the expression for the number of buttons in each box we first need to attribute a variable to that value, in this case we will use "x". The number x will be given by the division of all the buttons she has by the number of boxes she wants to organize them in. We have:
x = (number of buttons)/(number of boxes)
x = 30/6 = 5 buttons per box
The expression will be x = 30/6 and she'll have 5 buttons in each box.
can some one pls Use elimination to solve each system of equations
2x - y = -1
3x - 2y = 1
Answer:
Correct answer: x = - 3 and y = - 5
Step-by-step explanation:
Given:
2 x - y = - 1
3 x - 2 y = 1
We will multiply first equation with number (- 2) and get:
- 4 x + 2 y = 2
then we add this equation to another and get:
- 4 x + 3 x = 2 + 1
- x = 3 / · (- 1)
x = - 3
now we replace x = - 3 in the first equation and get:
2 (- 3) - y = - 1 ⇒ - 6 - y = - 1 / ·(- 1) ⇒ 6 + y = 1 y = 1 - 6 = - 5
y =- 5
God is with you!!!
Answer:
x= -3
y= -5
Step-by-step explanation:
-2 (2x-y= -1) = -4x + 2y = 2
-4x + 2y = 2
3x - 2y = 1
-------------------
-x = 3
x = -3
plug the x= -3 into the equation to find y
An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary. How much is her new salary
Answer:
$40,500 I took a test and this was the answer to the question.
Answer:
$40500
Step-by-step explanation:
Hey, please answer the attachment questions. 3 questions.
Answer:
A. Cat
B. 8
C. 6 people
Step-by-step explanation:
A. Just by looking at it Cat has the least amount of squares
B. There are 10 full squares in total (including the pieces). 80 people divided by 10 boxes is 8.
C. There is 1/2 and 1/4 more people who picked giraffe more than dogs. 1
1/2 of 8 is 4. 1/4 of 8 is 2. 4+2 = 6.
Sum of the odd integers between 30 & 54
Answer:
504
Step-by-step explanation:
The sum of the odd numbers between 30 and 54 will be 504.
What are the numbers?A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.
Given numbers are 30 and 54. The sum of the odd integers will be calculated by using the formula below:-
Sn = ( n / 2 ) [ a1 + a2 ]
The total numbers between 30 and 54 will be 12.
Sn = ( 12 / 2 ) [ 31 + 53 )
Sn = 6 x ( 84 )
Sn = 504
Therefore, the sum of the odd numbers between 30 and 54 will be 504.
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Alice, Betty and Carol all have the same amount of money (more than 50 cents but less than a dollar). Alice has two coins, Betty and Carol each have 3 coins, but Betty and Carol do not have any coins that are the same. How much money does each girl have?
Answer:
Each girl has 60 cents.
Step-by-step explanation:
Since they have between 50 cents and 1 dollar, then Alice should have a 50 cent coin and 1 coin of less value (because if she had 2 coins that are worth 25 cents or less, she would have only 50 cents at most).
On the other hand, Both betty and carol need to have a coin that is at least 25 cents worth (because otherwise they would have 30 cents at most), but since they cant have the same coins, then one of them should have one 50 cent coin (and 2 small cent coins) and the other should have at least two twenty five cent coins.
Lets assume that Betty has a 50 cent coin and Carol has two 25 cent coins. Since Alice also has a 50 cent coin, then the remaining coin of Alice should have the same value than the sum of the remaining 2 coins that Betty has.
The values of the coins are 5,10, 25, 50, and 100. Since they cant have 1 dollar coins, then the only possibility for a coin to have the sum of the values of 2 coins is to have a value of 10 (10 = 5+5). Thus:
Alice has one coin of 50 cents and one coin of 10 centsBetty has one coin of 50 cents and two coins of 5 centsCarol has two coins of 25 cents and one coin of 10 centsEach girl has 50+10 = 50+5+5=25+25+10 = 60 cents
In the right triangle shown, measure of angle A equals 45 degrees and the measure of AB equals 12. How long is BC?
Answer:
think ab = 4
Step-by-step explanation:
Santiago receives $143 per year in simple interest from three investments. Part is invested at 2%, part at 3%, and part at 4%. There is $500 more invested at 3% than at 2%. The amount invested at 4% is three times the amount invested at 3%. Find the amount of each rate
Please answer I need a lot of help on this!!!
Answer:
02a+.03b+.04c=126,
b=a+500,
c=3b
a=300., b=800., c=2400.
Step-by-step explanation:
The amount of each rate of interest given the total simple interest received is
$400, $900 and $2,700 respectively
let
a = 2% investment
= 0.02
b = 3% investment
= 0.03
c = 4% investment
= 0.04
Total interest = (0.02×a) + (0.03×b) + (0.04×c)
143 = 0.02a + 0.03b + 0.04c (1)
b = a + 500 (2)
c = 3b (3)
substitute (3) into (1)
143 = 0.02a + 0.03b + 0.04(3b)
143 = 0.02a + 0.03b + 0.12b
0.02a + 0.15b = 143 (4)
from (2)
b - a = 500 (5)
multiply (5) by 0.02
0.02b - 0.02a = 10
0.02a + 0.15b = 143 (4)
Add
0.02b + 0.15b = 10 + 143
0.17b = 153
b = 900
substitute b into (3)
c = 3b (3)
c = 3(900)
c = 2700
Recall,
b = a + 500 (2)
900 = a + 500
900 - 500 = a
a = 400
Therefore, the amount of each rate of interest given the total simple interest received is $400, $900 and $2,700 respectively
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There are 14 girls and 2 boys taking karate lessons. Write the ratio that compares the number of girls taking karate lessons to the total number of students taking karate lessons
Answer:
The correct answer is 7 : 8.
Step-by-step explanation:
There are 14 girls and 2 boys taking karate lessons.
Total number of students taking the karate class is 16.
The ratio that compares the number of girls taking karate lessons to the total number of students taking karate lessons is given by 14 : 16 = 7 : 8.
This can be interpreted as for every 8 students in the karate lesson, 7 of them are girls.
A car moves at 45 miles per hour. The time and the distance it travels are recorded.
What is the dependent variable?
the car
the time
the distance
45
Answer:
the distance
Step-by-step explanation:
More time care travels, more distance it goes. So distance depends of the time.
A county is considering rasing the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour. a random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour. at alpha equals 0.10, do you have enough evidence to support the county's claim? complete parts (a) through (d) below.
Answer:
No, at alpha equals 0.10, we do not have enough evidence to support the county's claim.
Step-by-step explanation:
We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.
A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.
Let [tex]\mu[/tex] = true mean speed of the vehicles.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30 miles per hour {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 miles per hour {means that the mean speed of vehicles is greater than 30 miles per hour}
The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean speed of 15 vehicles = 31 mph
s = sample standard deviation = 4.7 mph
n = sample of vehicles = 15
So, test statistics = [tex]\frac{31-30}{\frac{4.7}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= 0.824
Hence, the value of test statistics is 0.824.
Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.
Before the coffee shop opens the employees bake 40 cookies which is 25 less than the number of donuts they make does the equation x+25=40 describe the situation if not write an equation that does and explain what the variable represents
Answer:
x-25 = 40
Step-by-step explanation:
Let the number of cookies made = x
The employees bake 40 cookies which is 25 less than the number of donuts they make
Number of Cookies is less than Number of Donuts by 25
Therefore the equation that describes the situation is given as:
x-25 = 40 where x is the number of cookies made.
Answer:
The equation is not correct
Step-by-step explanation:
Lets break it down
Cookies = 40
Donuts lets call it x since we dont have a figure
It is said that the 40 cookies is 25 less than the number of donuts
So therefore
x less than 25 = 40
x-25=40
To get x we add 25 to each side
x-25+25=40+25
x=65
Equation should be
x-25=40
That is 65-25 =40
If m + n = m, what is the value of n?
a. 1
b. 0
C.-1
d.not enough information to tell
Answer:
B. 0
Step-by-step explanation:
if n is anything but 0 then the answer wouldn't be m it would be for example m - 1 or m + 1
for it to remain m then n must be 0
Can you guys answer this question ASAP, thanks will give brainliest
Answer:
J=10
S=6
Step-by-step explanation:
20j+25s=350
j=s+4
are the equations in the system of equations.
If you substitute them into each other they give you your answer.
Answer:
10 ; 6
Step-by-step explanation:
Ironed by Sydney:
25t
Ironed bu Jordan:
20(t+4) = 20t+80
25t + 20t + 80 = 350
45t = 270
t = 6
Jordan: 6 + 4 = 10
Evaluate 8j - k + 14 when j = 0.25 and k = 1.
Steps to solve:
8j - k + 14; j = 0.25 and k = 1
~Substitute
8(0.25) - (1) + 14
~Simplify
2 - 1 + 14
~Subtract
1 + 14
~Add
15
Best of Luck!
Answer:
[tex]8j - k + 14 \\ 8 \times0 .25 - 1 + 14 \\ 2 - 1 + 14 \\ 1 + 14 = 15[/tex]
hope this helps you...
Find the surface area of the cube shown below 2 1/2
Answer:
37.5
Step-by-step explanation:
Answer:
37.5
Step-by-step explanation:
3. Solve each division problem (reduce if possible):
1/5 divided by 1/10
Answer:
2
Step-by-step explanation:
Because to divde to fractions you multiply the first fraction by the second’s reciprocal. The reciprocal is when you switch the numerator and the denominator.In this case 1/5 times 10/1 which is 2.
You own 4 different shorts, 5 different t-shirts and 5 different caps. If
you want to wear one of each,
How many different combinations of clothing do you have?
combinations
Answer:
5
xD
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
Multiply 4, 5 and 5 which gives 100.
i really struggle with these kinda of questions oops
SOLVE
4(5x-2)=2(9x+3)
thanks
Step-by-step explanation:
4(5x-2) = 2(9x+3)
20x-8 = 18x+6
20x-18x = 6+8
2x=14
x= 14/2
∴ x= 7 [ANS]
Verify the identity. StartFraction sine (alpha plus beta )Over cosine alpha cosine beta EndFraction equals tangent alpha plus tangent beta Rewrite the numerator on the left side of the identity using one of the sum and difference formulas. StartFraction nothing Over cosine alpha cosine beta EndFraction Rewrite the fraction from the previous step such that it is a sum or difference of two expressions. Do not simplify the result. nothing Divide out any common factors in the expression from the previous step. nothing The expression from the previous step then simplifies to tangent alpha plus tangent beta using what? A. Quotient Identity B. Reciprocal Identity C. Even-Odd Identity D. Pythagorean Identity
Answer:
(A)Quotient Identity
Step-by-step explanation:
To Prove: [tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\tan \left(\alpha +\beta \right)[/tex]
Rewrite the numerator on the left side of the identity using the sum and difference formulas.
[tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\dfrac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta -\sin \alpha \sin \beta }[/tex]
Next, Divide the numerator and denominator by[tex]cos\alpha \text{cos}\beta[/tex]
[tex]=\dfrac{\frac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta }}{\frac{\cos \alpha \cos \beta -\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Rewrite the fraction from the previous step such that it is a sum or difference of two expressions as shown below
[tex]=\dfrac{\frac{\sin \alpha{\cos \beta }}{\cos \alpha{\cos \beta }}+\frac{{\cos \alpha }\sin \beta }{{\cos \alpha }\cos \beta }}{\frac{{\cos \alpha }{\cos \beta }}{{\cos \alpha }{\cos \beta }}-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Divide out any common factors in the expression from the previous step.
[tex]=\dfrac{\frac{\sin \alpha }{\cos \alpha }+\frac{\sin \beta }{\cos \beta }}{1-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
The expression from the previous step then simplifies to [tex]\tan \left(\alpha +\beta \right)[/tex] using the Quotient Identity
[tex]=\dfrac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\tan \left(\alpha +\beta \right)[/tex]
At a baseball game, 95% of people attending were supporting the home team, while 5% were supporting the visiting team. If the total number of people attending the game was 1000, how many people attending were supporters of the home team?
Answer:
950 people
Step-by-step explanation:
95% of people attending supported the home team.
1000 people attended the game.
That means that 95% of 1000 people supported the home team.
We need to find 95% of 1000.
To find a percent of a number, multiply the percent by the number. First, change the percent into a decimal by by moving the decimal point two places to the left. Then multiply the percent written as a decimal by the number.
95% of 1000 =
= 95% * 1000
= 0.95 * 1000
= 950
Answer: 950 people
A license plate is to consist of 5 digits followed by 5 uppercase letters. Determine the number of different license plates possible if the first and second digits must be odd, and repetition is not permitted.
Answer:
[tex]5.3044992\times 10^{10}[/tex]
Step-by-step explanation:
We are given that a license plate consist of 5 digits and 5 uppercase letters
Digits used=0,1,2,..9
Total number of letters=26
Repetition is not allowed
Total number of odd digits=(1,3,5,7,9)=5
The first place filled by 5
Second place filled by 4
Third place filled by 8
Fourth place filled by 7
Fifth place filled by 6
Sixth place filled by 26
Seventh place filled by 25
Eighth place filled by 24
Ninth place filled by 23
Tenth place filled by 22
Total number of possible different license plates =[tex]5\times 4\times 8\times 7\times 6\times 26\times 25\times 24\times 23\times 22[/tex]=[tex]5.3044992\times 10^{10}[/tex]
The number of possible license plates, considering the restrictions on the first and second odd digits and no repetition, is 53,144,832,000. This was determined by systematically calculating the choices for each digit and letter and then multiplying them together.
Calculating the Number of Different License Plates
To determine the number of different license plates possible, we need to consider two sections: the digits and the letters. The first and second digits must be odd, and repetition of digits and letters is not permitted.
Step-by-Step Calculation:
→ First digit: Since it must be odd (1, 3, 5, 7, 9), there are 5 choices.
→ Second digit: Also must be odd but different from the first, so there are 4 remaining choices.
→ Third digit: Any digit except the first two, leaving 8 choices.
→ Fourth digit: Any remaining digit, leaving 7 choices.
→ Fifth digit: Any remaining digit, leaving 6 choices.
→ First letter: Any uppercase letter, 26 choices.
→ Second letter: Any remaining uppercase letter, 25 choices.
→ Third letter: Any remaining uppercase letter, 24 choices.
→ Fourth letter: Any remaining uppercase letter, 23 choices.
→ Fifth letter: Any remaining uppercase letter, 22 choices.
→ Multiply these choices together:
5 × 4 × 8 × 7 × 6 × 26 × 25 × 24 × 23 × 22
→ Calculate the total:
5 × 4 × 8 × 7 × 6 = 6720
26 × 25 × 24 × 23 × 22 = 7893600
6720 × 7893600 = 53,144,832,000
Therefore, the number of different license plates possible is 53,144,832,000.
What is the value of the expression below?
√16 + 5 *1
Answer:
9
Step-by-step explanation:
√16=4
5*1=5
4+5=9
hope this helps
A water bottle has a label that is 3.5 inches high. If the bottle has a radius of 2 inches, how much paper would be needed to put labels on one dozen water bottles?
Answer:
527.52 in2 of paper.
Step-by-step explanation:
The area of the water bottle label can be calculated by the product of its circunference length and its height.
The length of its circunference is calculated as:
C = 2 * pi * r
C = 2 * 3.14 * 2 = 12.56 inches
Now, to find the area of the label, we just multiply the length by the height:
Area = C * h = 12.56 * 3.5 = 43.96 in2
As we want to know the amount of paper for 12 water bottles, we multiply the area of one label by 12:
Total Paper = 12 * 43.96 = 527.52 in2
It will be needed 527.52 in2 of paper.
Solve the inequality below; Which direction will the graph go in and will the dot be open or closed? m+5>-1
Answer:
The dot will be closed, and to the right from -6
Step-by-step explanation:
We can rearrange [tex]m+5>-1 = -6 < m[/tex]
As it is only a < we close the dots. It must go to the left as m is greater than -6 - all numbers greater than a value will be to the right on the number line.