The number of co-workers that like gumdrops and chocolate is 7 (option b).
How many like chocolate and gumdrops?The mathematical operations that would be used to determine the answer are addition and subtraction.
Addition is determining the total value or summing two or more numbers. The sign used to represent addition is +. Subtraction is the process of determining the difference between two or more numbers. The sign used to denote subtraction is -.
The first step is to add the total number of people who like a particular type of candy : 10 + 8 + 2 + 3 + 5 = 28
The second step is to subtract that number gotten in the previous step from the total number of co-workers.
Co-workers that like both chocolate and gum drops = 35 - 28 = 7
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In the figure, m∠AOD=105. If m∠AOB=8x, m∠BOC=7x and m∠COD=6x, what is the value of x?
Answer:
x = 5
Step-by-step explanation:
from the diagram
∠ AOB + ∠ BOC + ∠ COD = ∠ AOD ( substitute values )
8x + 7x + 6x = 105
21x = 105 ( divide both sides by 21 )
x = 5
Answer:
5
Step-by-step explanation:
AOB+BOC+COD=AOD
6x+8x+7x=105
21x=105
x=105÷21
x=5
a boy throws a baseball across a field. the ball reaches its maximum height, 18 meters, after 1 second. after approximately 2.3 seconds, the ball lands on the ground. the ball’s motion can be modeled using the function f(x)
The height of the ball after 1.5 seconds is 15.5 meters so option (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
Given the function as the height of ball f(x) and time x
f(x) = -10x² + 20x + 8
At x = 1.5
f(1.5) = -10(1.5)² + 20(1.5) + 8
f(1.5) = 15.5
Hence "The height of the ball after 1.5 seconds is 15.5 meters".
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Given question is incomplete complete question is attached below image ;
What is the simple interest paid if $900 principal 6% interest rate for 2 year
Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.
The simple interest for $900 at an interest rate of 6% is $108.
What is simple interest?Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.
We have,
Principal = $900
Rate of interest = 6%
Time = 2 years.
Remember that time should always be in years.
The formula for simple interest is given by:
SI = PRT / 100
Where,
P = principal
R = rate of interest
T = Number of years
So,
SI = 900 x 6 x 2 / 100
SI = $108
Thus the simple interest for $900 at an interest rate of 6% is $108.
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25 points plus brainliest
Answer:
[tex]|4x+3|+7 < 10[/tex]
Step-by-step explanation:
When you evaluate the expression, you get [tex]-\frac{3}{2} < x < 0[/tex]
A 3.5 ft child casts a 60 inch shadow, the child is next to a telephone pole that casts a 50 ft shadow how tall is the telephone pole
The telephone pole is 35ft tall .
What is height?The height of any object is define as the distance measurement of that object from the top to its base. In geometry it is also called as altitude.
Height can be measured in various quantities such as feet, inches, centimeters etc.
Some of measurements are as below.
feet to inches1 feet = 12 inches
feet to centimeters1 feet = 30.48 cm
inches to centimeters1 inch = 2.54 cm
meters to feet1 feet = 3.28 feet
In the given question,
Convert 60 inches to feet ,
60 inches = 60/12 feet = 5 feet
Given, pole shadow = 50ft
child height =3.5ft
now, Set up proportion between the ratios of the child and his shadow and the telephone pole and its shadow.
[tex]\frac{child \ height}{child \ shadow \ length} =\frac{pole \ height}{pole \ shadow \ length}[/tex]
Let, x be pole height
=> [tex]\frac{3.5}{5} =\frac{x}{50}[/tex]
now solve the equation,
3.5 ×50 = x × 5
x = 35
Thus, the pole is 35 feet tall.
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Melody works at The Accokeek Ice Cream Hut. She earns $14 per hour. This week,
her boss had to cut her schedule, so she only worked 80% of the number of hours
she normally works. However, to compensate her, she was given a bonus of $30.
At the end of the week, Melody had earned $198.
The number of hours Melody worked this week was 15.
The hourly earnings of Melody at the Accokeek Ice Cream Hut are $14.Let the number of working hours in a week be "x".The number of hours Melody actually worked this week is 80 percent of "x".The number of hours Melody actually worked this week is 0.8x.The amount of compensation Melody received is $30.The total amount Melody earned at the end of the week was $198.The amount Melody should get at the end of the week is the sum of the compensation amount and the earnings for the number of hours she worked.198 = 30 + 14*0.8x168 = 11.2xx = 15Thus, Melody worked for 15 hours.To learn more about percent, visit :
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On a coordinate plane, 2 straight lines are shown. The first solid line is horizontal at y = negative 1. Everything above the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 1) and (0, 0). Everything below the line is shaded.
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?
Using a linear function, one constraint on the inequality is given by:
y < -0.5x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points, the slope is given by change in y divided by change in x.
For the line in the inequality, the points are:
(-2,1) and (0,0).
Hence the slope is given by:
m = (0 - 1)/(0 - (-2)) = -1/2 = -0.5.
Hence:
y = -0.5x + b.
When x = 0, y = 0, meaning that the y-intercept is of b = 0, and:
y = -0.5x.
Everything below the line is shaded, meaning that the values of y that are less than the line are shaded, and the inequality is:
y < -0.5x.
The inequality is only less, not less or equal, because the line is dashed and not solid.
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miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. the area of the reduced photo is 64 square inches. in the equation (x – 3)2
Original sides of the square before reducing was 11 inches.
What is a quadratic equation ?A quadratic equation has highest degree of two and it has 2 roots.
According to the given question Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album.
Assuming sides of the square to be x inches.
∴ From the given data
( x - 3 )( x - 3 ) = 64 ( area of a square is product any two sides )
x² - 6x + 9 = 64
x² - 6x - 55 = 0
x² - 11x + 5x - 55 = 0
x( x - 11 ) + 5( x-11 ) = 0
(x - 11 )( x + 5) = 0
∴ x = 11 or x = -5. ( length of something can not be negative )
So, the original length of the sides of the square is 11 inches.
Original area is
= (11×11)
= 121 sq inches.
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2 is subtracted from the product of 5 and a number
Answer:
2 - 5 = -3.
Step-by-step explanation:
I subtracted two from five and got negative three lol
Two interior decorating teams are competing in a kitchen remodel competition. Their remodels are graded on the following categories, each worth 18 points; time to complete, design, and total cost. Time to complete is worth 75% of their final score, design is 15%, and total cost is 10%. Whoever has the largest final score wins $150,000. Suppose Team A received 15 points for time to complete, 9 points for design, and 14 points for total cost. Suppose Team B received 17 points for time to complete, 7 points for design, and 13 points for total cost. Using technology, determine which team won the competition. Team A won by 1.9 points. Team A won by 1.1 points. Team B won by 1.9 points. Team B won by 1.1 points.
Answer:
listen there is a lack of information the information you give isn't enough
The correct answer is Team B won by 1.1 points.
To determine which team won the competition, we need to calculate the final scores for both Team A and Team B based on the given weights for each category and the points they received in each category.
For Team A:
- Time to complete (75% of 15 points) = 0.75 * 15 = 11.25 points
- Design (15% of 9 points) = 0.15 * 9 = 1.35 points
- Total cost (10% of 14 points) = 0.10 * 14 = 1.4 points
Total score for Team A = 11.25 + 1.35 + 1.4 = 14 points
For Team B:
- Time to complete (75% of 17 points) = 0.75 * 17 = 12.75 points
- Design (15% of 7 points) = 0.15 * 7 = 1.05 points
- Total cost (10% of 13 points) = 0.10 * 13 = 1.3 points
Total score for Team B = 12.75 + 1.05 + 1.3 = 15.1 points
Now, we compare the total scores of both teams. Team A has a total score of 14 points, while Team B has a total score of 15.1 points. Therefore, Team B won by 1.1 points.
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1 Compare the coordinates of the corresponding vertices of ALMN and AL'M'N' in
the Example. Describe the effect of the 270° counterclockwise rotation on the
vertices. What other rotation of ALMN would have the same effect?
10. A line passes through points (4, 18) and (6x,2k). What is the slope of the line?
8k-9
12x-4
A
B
2k-9
6x-4
C
D
k-9
3x-2
2k-9
3x-4
The slope of the line which passes through the points (4, 18) and (6x, 2k) is (k - 9)/(3x - 2).
According to the given question.
A line passes through points (4, 18) and (6x,2k).
Which means we have two points (4, 18) and (6x,2k).
As we know that, the slope of a line is the ratio of the amount that y increases as x increases some amount.And the slope formula is m=(y2-y1)/(x2-x1) if a lines passes through the point (x2, y2) and (x1, y1).
Therefore, the slope of the line which passes through the points (4, 18) and (6x,2k)
= 2k - 18/ 6x - 4
= 2[k - 9]/2[3x - 2]
= (k-9)/(3x - 2)
Hence, the slope of the line which passes through the points (4, 18) and (6x, 2k) is (k - 9)/(3x - 2).
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CAN SOMEONE PLS HELP ME W THIS ONE PROBLEM ASAPPPP I RLLY NEED HELP
segment XY has a midpoint at M. The coordinates of X are (3,4) and the coordinates of M are (5,0). what are the coordinates of endpoint y?
endpoint y would be
(7,-4)
because when you graph all 3 points
(7,-4) adds nicely to the line that the other 2 make
in a geometric series, the sum of the first three terms is 14.25 and the sum of the first four terms is 24.375. find the exact value of the first term and the common ratio. give your answer in the format ‘u1,r’, without spaces.
The first term of the Geometric Series = 3 and its common ratio = 3/2.
What is a geometric Series?An unlimited number of terms with a fixed ratio between each term make up a geometric series.
For 'n' termed GP with a = first term and r = common ratio, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex]
Given:
Sum of first three terms of a G.P. = 14.25Sum of first four terms of the G.P. = 24.375To find: First term of the GP and the common ratio.
Finding:
As, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex], for n =3,
[tex]S_{3}=\frac{a(r^{3}-1)}{r-1}=14.25[/tex] (eqn 1)
=> Similarly for n = 4,
[tex]S_{4}=\frac{a(r^{4}-1)}{r-1} = 24.375[/tex]
On dividing [tex]S_3 by S_4[/tex], we get:
[tex]\frac{14.25}{24.375}=\frac{r^{3}-1}{r^{4}-1}[/tex]
=> On solving the equations, we get:
[tex]14.25r^{4}-24.375r^{3}+10.125=0[/tex]
r = 3/2 (on factorizing the equation)
Now, substituting this in eqn 1
=> [tex]14.25=\frac{a((\frac{3}{2})^{2}-1)}{\frac{3}{2}-1}[/tex]
=> a = 3 on further solving the equation for a.
Hence, the first term of the Geometric Series = 3 and its common ratio = 3/2.
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2p=47−17 please help with explinations
We calculate the right side of the equation : 47 - 17 = 30
2p = 30
Divide both side by 2, we have : p/2 = 30/2 -> p = 15.
Answer:
P=15
Step-by-step explanation:
2p = 47-17
2p = 30
Divide both sides by the coefficient of p which is 30
[tex]\frac{2p}{2} =\frac{30}{2}[/tex]
P= 15
what is the perimeter of a polygon that has the coordinates of (-3,2) (2,2) (2,-4) (-1,-4) (-1,-2) (-3,-2) (-3,2)
The perimeter of a polygon is 24 units.
In this question, we have been given the coordinates of a polygon.
we need to find the perimeter of a polygon.
Let A= (-3,2), B = (2,2), C = (2,-4), D = (-1,-4), E = (-1,-2), F = (-3,-2)
First we find the length of each side of a polygon.
|AB| = √5² + 0²
|AB| = 5
|BC| = √0² + (-6)²
|BC| = 6
|CD| = √(-3)²+0²
|CD| = 3
|DE| = √0²+2²
|DE| = 2
|EF| = √(-2)²+0²
|EF| = 2
|FA| = √0²+4²
|FA| = 4
The perimeter of a polygon would be,
P = AB + BC + CD + DE + EF + FA
P = 5 + 6 + 3 + 2 + 2 + 4
P = 24 units
Therefore, the perimeter of a polygon is 24 units.
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In the rectangle shown below, the length is longer than its width w. List all the possible
whole number dimensions for the rectangle, and name the dimensions that give the smallest
perimeter.
Area is 40 m2
Answer: w can be 1,2,4,5
Step-by-step explanation:
Let's recap the formula of Area:
Area = width x length = w x l
Area = 40 = w x l
The definition of a whole number: is a number without fractions; an integer such as 0, 1, 2, 3, 4, 5, 6,...
Let's start with 0. 0 times anything is equal to 0, so we cannot make 40 out of zero. Cross this out.
Next, let's try with 1:
a. 1x40 = 40
Then, applying the same concept to the rest we have these multiplications:
b. 2x20 = 40
c. 4x10 = 40
d. 5x8 = 40
e. 8x5 = 40
f. 10x4 = 40
g. 20x2 = 40
h. 40x1 = 40
Let's recap the formula of Perimeter:
P = 2 x (w + l)
So, we have the calculated perimeters (according to the above finding):
a. P= 2x(1+40)=82
b. P= 2x(2+20)=44
c. P= 2x(4+10)=28
d. P= 2x(5+8)=26
The below answers do not fit the [width < length]
e. P= 2x(8+5)=26 [not an answer]
f. P= 2x(10+4)=28 [not an answer]
g. P= 2x(20+2)=44 [not an answer]
h. P= 2x(40+1)=82 [not an answer]
Compare square root of one hundred seventy and one hundred six eighths using <, >, or =.
square root of one hundred seventy is greater than one hundred six eighths
square root of one hundred seventy is equal to one hundred six eighths
one hundred six eighths is less than square root of one hundred seventy
one hundred six eighths is greater than square root of one hundred seventy
Square root of one hundred and seventy is greater than square root of one hundred and sixty eight.
What is a perfect square number ?A perfect square number is a number which when taken square root comes out as an integer.Every number which is not a perfect square when taken square root of it is irrational number.We can obtain square root of a perfect square number by prime factorisation method.
Given we have to compare [tex]\sqrt{170}[/tex] and [tex]\sqrt{168}[/tex].
We know that if the square roots are not given then we have easily concluded that 170 > 168.Same in the case of square root:
[tex]\sqrt{170} > \sqrt{168}[/tex].
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Which angle is supplementary to LSM?
A.OSN
B.SLM
C.LSM
D.MSN
Answer:
D.MSN
Step-by-step explanation:
Supplementary angles complete each other to 180° and they are on a straight line.
We are asked to find the supplementary angle to angle LSM on figure 2.
Amongst given options we see angle LSM and angle MSN make a straight line therefore they are supplementary angles.
10. Solve the equation by completing the square. Round to the nearest hundredth if necessary. x²-3x - 3=0
-3.75, 6.75
2.72,0.28
0.87, 2.29
3.79,-0.79
The roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.
Given that the equation is [tex]x^{2}[/tex]-3x-3=0.
We are required to find the roots of the equation by completing the square method.
Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation,cubic equation and many more depending on the power of the variables that are present in the equation.
The equation is [tex]x^{2}[/tex]-3x-3=0.
[tex]x^{2}[/tex]-3x=3
[tex](x+3/2)^{2}[/tex]=-(c-[tex]b^{2}[/tex]/4)
So,
[tex](x-3/2)^{2}[/tex]=-[-3-[tex](-3)^{2}[/tex]/4]
[tex](x-3/2)^{2}[/tex]=-[-3-9/4]
[tex](x-3/2)^{2}[/tex]=21/4
x-3/2=±[tex]\sqrt{21}[/tex]/2
x=([tex]\sqrt{21}[/tex]+3)/2,(-[tex]\sqrt{21}[/tex]+3)/2
x=(4.58+3)/2, (-4.58+3)/2
x=7.58/2, -1.58/2
x=3.79,-0.79
Hence the roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.
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Answer:
by completing the square method the answer is 3.79 and -0.79.
Step-by-step explanation:
above
21. a. What four factors were used to create this Product Game board?
9 15 18
21 ? 30 35 Factors:
36 42 49
b. What product is missing from the grid?
What is the missing number from the grip I need help
The four factors were used to create this Product Game board are {2, 3, 5, 7} and the product missing from the grid is 25
To see what are factors are used in the given list, we just need to write each of the numbers, as a product of prime factors such as 2, 3, 5, 7 .
9 = 3* 3
15 = 3 *5
18 = 3 *2*3
21 = 7*3
30 = 5*3*2
35 = 7*5
36 = 3*3*2*2
42 = 2*3*7
49 = 7*7
As we can see, the 4 factors used to product the numbers in the given list are {2, 3, 5, 7}
for the second part that is to find the missing number between 21 and thirty we first need to write all the numbers between 21 and thirty and check which number is having the only factors of at least one of (2,3,5,7)
the numbers are 22 , 23 ,24, 25 ,26 ,27 ,28, 29
After checking the missing number is 25(5*5) because there has to be at least 4 products who have same factor and 5 is the factor who has appeared only three times
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Ax-5=19
I need help solving this problem?
They are 9 guitars sold in a week with a total of 3,611 dollars. Electrics are 479 each and acustics are 339 each. How many of each guitars were sold"?
MARKING BRAINLEIST IF CORRECT
Answer choices:
1. Alternate Interior Angles Theorem; 2 Definition of Congruence
1. Alternate Exterior Angles Theorem; 2. Substitution Property
1. Definition of Congruence; 2. Alternate Interior Angles Theorem
1. Substitution Property; 2. Alternate Exterior Angles Theorem
Answer:
I think it's B (or A?)
Step-by-step explanation:
For alternate interior, they are alternate interior angles
Then for 2, they are equal and congruent, but they are SUBSTITITUING the angle numbers to the equation.
pls brainliest if I'm right :D
Rationalize the denominator
-x5
√12x - 9
Answer:
Step-by-step explanation:
-2x^6-9
please give me the brainliest
Find the area of the figure. Write the answer is radical form
The Area of the given figure in the radical form is [tex]96\sqrt[4]{x^{9} }[/tex] .
Area of a rectangle can be found by using the formula
Area = length*breadth
in the given question
length of the rectangle
= [tex](4x)^{\frac{3}{2} }[/tex]
On simplifying we get
[tex](4x)^{\frac{3}{2} }=(2^{2} x)^{\frac{3}{2} }\\ \\ =2^{2*\frac{3}{2} } *x^{\frac{3}{2} } }[/tex] ( as (a.b)ⁿ=aⁿ.bⁿ )
[tex]=2^{3} *x^{\frac{3}{2} } }\\ \\ =8*x^{\frac{3}{2} } }[/tex]
breadth of the rectangle = [tex]12x^{\frac{3}{4} }[/tex]
The required area = length * breadth
Substituting the values we get
Area = [tex]8*x^{\frac{3}{2} } }[/tex] * [tex]12x^{\frac{3}{4} }[/tex]
=96*[tex]x^{\frac{3}{2}+\frac{3}{4} }[/tex]
taking LCM of exponents as 4 and solving further we get ,
=[tex]96x^{\frac{9}{4} }[/tex]
Expressing in radical form we get ,
Area = [tex]96\sqrt[4]{x^{9} }[/tex]
Therefore , the Area of the figure in the radical form is [tex]96\sqrt[4]{x^{9} }[/tex] .
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Caroline is driving to a concert and needs to pay for parking. there is an automatic fee of $5 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. how much total money would caroline have to pay for parking if she left her car in the lot for 3 hours? how much would caroline have to pay if she left her car in the lot for t hours?
The total money Caroline would have to pay for parking if she left her car in the lot for 3 hours is $11
For t hours the Caroline would pay 5+2t
What is algebraic expression?
Algebraic expression is a mathematical statement which points to when operations such as addition, subtraction, multiplication as well as division, are used for variables and constants, in essence, using algebraic expression, we can derive the equation that gives the total cost of Caroline driving and using the parking lot at the concert
There is a fixed charge of $5, there is also an additional $2 for every spent, if represent hours spent by t, then she would pay 2t in total for using the parking lot.
Total cost=5+2t
when t=3 hours
total cost=5+(2*3)
total cost=$11
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They spent $150 to rent a bounce house for 4 hours. How much is the hourly rate for the rental?
Show your work using the long division algorithm.
Answer:
$37.50
Step-by-step explanation:
consider measurements of the width w and length l of a piece of paper used to calculated the area of the paper using a
The area of the piece of paper is;
Area = length x width
⇒ a = l w unit square.
Here,
Given that;
The width of piece of paper = w
The length of piece of paper = l
We have to find the area of piece of paper by using a.
What is Area of rectangle?
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
Now,
Consider the shape of piece of paper is rectangular.
The width of piece of paper = w
The length of piece of paper = l
Since, we know that;
Area of rectangle = length x width
Then, The Area of piece of paper 'a' = length x width
⇒ a = l * w
Where, a = Area of rectangle, l = length of piece of paper and
w = width of rectangle.
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Can anyone answer these for me?
Answer:
x=12 y=10 z=-12
Step-by-step explanation: