Answer:
The smaller number is 11 and the larger number is 16.
Step-by-step explanation:
Let x = smaller number and y = larger number. The sum of these numbers is 27, so we can make the equation x + y = 27. Twice the smaller number (2x) plus three times the larger number (3y) is 70, so we can also make the equation 2x + 3y = 70.
Now, let's take a look at that first equation, x + y = 27. Let's isolate y on one side, giving us y = -x + 27. Now, we can replace y in the second equation with that value, which will allow us to solve for x.
2x + 3y = 70
2x + 3(-x + 27) = 70
2x - 3x + 81 = 70
-x + 81 = 70
-x = -11
x = 11
So, the smaller number is 11. Again, our original equation is x + y = 27. We can now replace x with 11.
11 + y = 27
y = 16
The larger number is 16. If you have any questions or found that really confusing, let me know and I'll try to clarify for you. :)
Going to store for Quetion‘s 9X -7 equals -7
The polynomial 9x-7=-7. The value is x=0.
Given that,
The polynomial 9x-7=-7
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. We are able to perform mathematical operations on polynomial expressions such addition, subtraction, multiplication, and positive integer exponents but not division by variables.
The terms Poly (meaning "many") and Nominal (meaning "terms") make form the word polynomial.
The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. So-called polynomial degrees are polynomial equations with one variable having the largest exponent.
9x-7=-7
9x=-7+7
9x=0
x=0
Therefore, The value is x=0
Complete question: The polynomial 9X -7 = -7. Find the value of x.
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“Rewrite the following expression so there are no negative exponents. Do not simplify”
The rule of the negative exponent is given below:
[tex]X^{-a}=\frac{1}{X^a}[/tex]Hence, the expression:
[tex]\frac{yx^3.-2x^{-2}y^{-2}}{-3x^{-1}y^{-4}.-3y^3}[/tex]can then be re-written, without the negative exponent, as:
[tex]\frac{yx^3\text{ . }\frac{-2}{x}\frac{1}{y^2}}{\frac{-3}{x}\frac{1}{y^4}.-3y^3}[/tex]2) The expression:
[tex]\begin{gathered} \frac{x^3y^{-1}}{3x^4y^{-2}.2x^2y^2} \\ \end{gathered}[/tex]can be re-written, without the negative exponent, as:
[tex]\frac{x^3\times\frac{1}{y}^{}}{3x^4\times\frac{1}{y^2}.2x^2y^2}[/tex]I need to know how to do the whole thing and understand it.
We are given the data on the number of candies handed by neighborhood A and neighborhood B.
Let us first find the mean and variance of each neighborhood.
Mean:
[tex]\bar{x}_A=\frac{\sum x}{N_1}=\frac{12}{6}=2[/tex][tex]\bar{x}_B=\frac{\sum x}{N_2}=\frac{20}{6}=3.33[/tex]Variance:
[tex]s_A^2=\frac{\sum x^2}{N_1}-\bar{x}_A^2=\frac{28}{6}-2^2=0.667[/tex][tex]s_B^2=\frac{\sum x^2}{N_2}-\bar{x}_B^2=\frac{80}{6}-3.33^2=2.244[/tex]A. Null hypothesis:
The null hypothesis is that there is no difference in the mean number of candies handed out by neighborhoods A and B.
[tex]H_0:\;\mu_A=\mu_B[/tex]Research hypothesis:
The research hypothesis is that the mean number of candies handed out by neighborhood A is more than neighborhood B.
[tex]H_a:\;\mu_A>\mu_B[/tex]Test statistic (t):
The test statistic of a two-sample t-test is given by
[tex]t=\frac{\bar{x}_A-\bar{x}_B}{s_p}[/tex]Where sp is the pooled standard deviation given by
[tex]\begin{gathered} s_p=\sqrt{\frac{N_1s_1^2+N_2s_2^2}{N_1+N_2-2}(\frac{N_1+N_2}{N_1\cdot N_2}}) \\ s_p=\sqrt{\frac{6\cdot0.667+6\cdot2.244}{6+6-2}(\frac{6+6}{6\cdot6})} \\ s_p=0.763 \end{gathered}[/tex][tex]t=\frac{2-3.33}{0.763}=-1.74[/tex]So, the test statistic is -1.74
Critical t:
Degree of freedom = N1 + N2 - 2 = 6+6-2 = 10
Level of significance = 0.05
The right-tailed critical value for α = 0.05 and df = 10 is found to be 1.81
Critical t = 1.81
We will reject the null hypothesis because the calculated t-value is less than the critical value.
Interpretation:
This means that we do not have enough evidence to conclude that neighborhood A gives out more candies than neighborhood B.
Ill send you the pictures of my question, it isnt allowing me to put them here
A is the correct option
Based on the table below, find the range of f(x) x 137911f(x) 8175209Range = {
The range of the functions is the set made of the f(x) values. Therefore the range is:
[tex]\lbrace8,17,5,20,9\rbrace[/tex]-2/5y=4 what is y???????
Answer:
-10
Step-by-step explanation:
solve for y by simplifying both sides of the equation, then isolating the variable.
find the area of the trapezoid __ m squared simplify the answer
A trapezoid is given with base lengths of 10m and 14m, and a height of 9m.
It is required to find the area of the trapezoid.
Recall that the area of a trapezoid with base lengths b₁, b₂, and height h is given by:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]Substitute b₁=14, b₂=10, and h=9 into the formula:
[tex]\begin{gathered} A=\frac{1}{2}(14+10)\cdot9 \\ \Rightarrow A=\frac{1}{2}\cdot24\cdot9=108 \end{gathered}[/tex]Hence, the required area is 108 m².
The answer is 108 m².
In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown. a. What is a function that relates the sales and the number of muffins?b. How many muffins would you have to sell to make at least $175.000 in sales?a. Write the function.s= ______. (Type and expression using m as the variable.)
The function is S = N*1.75. The number of muffins that must be sold to earn $175 is 100.
The number of muffins sold and the amount of sales in a bake sale are shown in the given table. The number of muffins sold is 12, 14, 17, and 18. The amount of the sale is $21, $24.5, $29.75, and $31.5. We can write these in the form of coordinates as (12, 21), (14, 24.5), (17, 29.75), and (18, 31.5).
We should first determine if the ratio is constant. The ratio is the division of the sales amount by the respective number of muffins sold. We find that the ratio of all the pairs is the same and is equal to 1.75. We can form an equation as given below :
S = N*1.75
The variables "S" and "N" represent the sales amount and the number of muffins, respectively. We need to find the number of muffins that need to be sold to earn $175.
S = N*1.75
175 = N*1.75
N = 100
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Lisa received a 70 gift card for a coffee store. She used it in buying some coffee that cost 8.49 per pound. After buying the coffee, she had 36.04 left on her card. How many pounds of coffee did she buy?
Initially she had 70 pounds in her gift card.
After buying her coffee she was left with 36.04 pounds.
Amount she spent on coffee is 70-36.04=34.96
One pound of coffee costs 8.49
To calculate how many pounds of coffee Lisa bought ->
34.96/8.49= 4
So in total she bought 4 pounds of coffee.
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Rick and Chumlee buy and sell sports collectibles. Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars. Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars. Let c be the cost
of each card and let b be the cost of an autographed baseball.
a) Write an equation relating the items bought by Rick:
b) Write an equation relating the items bought by Chumlee:
c) Solve the system above using substitution and interpret in context:
The cost of a card is
dollars.
dollars and the cost of a baseball is
a) equation relating the items bought by Rick is
14c + 13 b = 263
b)equation relating the items bought by Chumlee
17c + 4b = 284
C) The cost of a card is 16
The cost of a baseball is 3
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical truths. It takes variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a meaningful mathematical statement. All branches of mathematics, including coordinate geometry, calculus, and trigonometry, employ algebra. A fundamental algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations like addition, subtraction, multiplication, division, etc. are done on variables and constants.
Rick and Chumlee buy and sell sports collectibles.
Let c be the cost of each card and let b be the cost of an autographed baseball.
Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars.
a) equation relating the items bought by Rick is
14c + 13 b = 263
Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars.
b)equation relating the items bought by Chumlee
17c + 4b = 284
C)
14c + 13 b = 263 .....(i)
17c + 4b = 284......(ii)
[tex]b = \frac{284-17c}{4}[/tex]
put the value of b in equation 1 you will get
14c +13([tex]\frac{284 - 17c}{4}[/tex])=263
56c + 3692 - 221c = 1052
175c = 2640
c = 16
[tex]b = \frac{284-17c}{4}[/tex].....(iii)
put the value of c in equation 3
b = [tex]\frac{284 - 17(16)}{4}\\ = \frac{12}{4}[/tex]
= 3
The cost of a card is 16
The cost of a baseball is 3
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Bath and Body works is having a sale. Their Body Mists are 65% off. If the original price is $14.50, how much would you spend if you bought 5 body mists? Write an equation(s) to represent the problem and solve.
Body mists are 65% off
The original price is $14.50
So, the 60% of 14.50 is
[tex]\begin{gathered} 60\text{ percent of 14.50 dollars is =}\frac{60\times14.50}{100} \\ 60\text{ percent of 14.50 dollars is}=8.7\text{ dollars} \end{gathered}[/tex]Since the 8.7 dollars is off so, the net price is 14.50-8.7
The prics of one body mists after 60% off is $5.8
Let the x is the amount spend in the 5 body mists
Since the prics of 1 body mists is $5.8
So, the price of 5 body mists is : 5 times of $5.8
[tex]\begin{gathered} \text{The price of 5 body mists =5}\times5.8 \\ \text{The price of 5 body mists=}29\text{ dollars} \\ \text{ Since we assume that the price of the 5 body mists is x } \\ So,\text{ x = 29 Dollars} \end{gathered}[/tex]Answer : x = $29
please help
A bird flying over water drops a crab from a height of 10 feet. The distance
the crab is from the water as it falls can be represented by d in the equation
d equals negative t to the power of 2 end exponent plus 10, where t is time in seconds. To catch the crab as it falls, a different
bird flies along a path represented by the equation d equals 5 t plus 5. In how many
seconds will the second bird catch the crab before it hits the water?
Solving a quadratic equation we can see that the second bird catches the crab after 0.85 seconds.
In how many seconds the second bird catches the crab?
The equation that describes the height of the crab is:
d = -t^2 + 10
The equation that represents the path of the second bird is:
d' = 5t + 5
The bird will be able to catch the crab when both are at the same height, this happens when:
-t^2 + 10 = 5t + 5
We need to solve this for t.
-t^2 + 10 - 5t - 5 = 0
-t^2 - 5t + 5 = 0
Using the quadratic formula we will get:
t = (5 ± √( (-5)^2 - 4*(-1)*5))/(2*-1)
t = (5 ± 6.7)/(-2)
We only care for the positive solution, which is:
t = (5 - 6.7)/(-2) = 0.85
So the bird catches the crab after 0.85 seconds.
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Solve the inequality and express your answer in intervalvenation use decimal form for numeric values
Given:
[tex]\frac{20}{4}<\frac{z+7}{2}<\frac{25}{4}[/tex]Required :
To solve this
Explanation:
[tex]\begin{gathered} first\text{ of all separate compound inequalities into system of inequalities} \\ \\ \frac{z+7}{2}>\frac{20}{4}\text{ }\frac{z+7}{2}<\frac{25}{4} \\ \\ reduce\text{ the fraction} \\ \\ \frac{z+7}{2}>5\text{ or z+7>2}\times5 \\ \\ z+7>10 \\ \\ z>10-7 \\ \\ z>3 \end{gathered}[/tex][tex]\begin{gathered} \frac{z+7}{2}<\frac{25}{4} \\ \\ multiply\text{ both sides of the inequality by the least common denominator} \\ \\ 4\times\frac{z+7}{2}<4\times\frac{25}{4} \\ \\ reduce\text{ the expression to the lowest term} \\ \\ 2(z+7)<25 \\ \\ 2z+14<25 \\ \\ 2z<25-14 \\ \\ z<\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} z>3\text{ and z <}\frac{11}{2} \\ \\ 3Required answer:3
multiply the question
EXPLANATION:
In order to multiply correctly we must follow the following steps:
-Multiply the numbers that are not in power of 10 and finally add the powers of 10.
The exercise is as follows:
[tex]undefined[/tex]what is 5.37 with 15% discount
Answer
5.37 with 15% discount = 4.5645
Explanation
5.37 with 15% discount
= 5.37 - (15% of 5.37)
= 5.37 - 0.15(5.37)
= 5.37 - 0.8055
= 4.5645
Hope this Helps!!!
Answer:
Step-by-step explanation:
15% off 5.37 is 4.56.
The difference is 0.81
Your company fireworks show is getting bigger, The boss has requested that the viewing area (which is 4 ft x 6 ft) be doubled; the parking area (which is 540 ft x 75 ft) be doubled; and the city ordinance requires the fireworks to be in the air less than 4 seconds and not go any higher than 600 feet.
Answer the following questions:
1. Determine the dimensions of the new viewing area. The existing area is 6 ft long by 4 ft wide.
2. Determine the dimensions of the new parking area. The existing area is 540 ft long by 75 feet wide.
3. Determine the height of the fireworks and how long they are in the air using the following equation:
ℎ= −500/9 t^2 + 1000/3 t + 10
The solution to the questions are
New viewing area dimension: 8 ft by 12 ftNew parking area dimension: 1080 ft by 150 ftHeight of fireworks: 510 unitsThe dimension of the new viewing areaFrom the question, we have the following parameters:
Initial dimension of the viewing area:
4 ft by 6 ft
The scale of dilation is given as
Scale = 2 (i.e. doubled)
Using the above as a guide, the new dimensions are calculated using
New = Old * Scale
So, we have
New = (4 ft by 6 ft) x 2
Evaluate
New = 8 ft by 12 ft
The dimension of the new parking areaThe given parameters are
Initial dimension of the parking area:
540 ft by 75 ft
We use the same scale factor as (a) i.e.
Scale = 2 (i.e. doubled)
Using the above as a guide, the new dimensions are calculated using
New = Old * Scale
So, we have
New = (540 ft by 75 ft) x 2
Evaluate
New = 1080 ft by 150 ft
The height of fireworksThe function is given as
ℎ= −500/9 t^2 + 1000/3 t + 10
Differentiate the function
So, we have
ℎ'= −1000/9 t + 1000/3
Set the differentiated function to 0
So, we have
−1000/9 t + 1000/3 = 0
This gives
1000/9 t = 1000/3
Multiply both sides by 9/1000
t = 3
Substitute 3 for t in ℎ= −500/9 t^2 + 1000/3 t + 10
ℎ = −500/9 x 3^2 + 1000/3 x 3 + 10
Evaluate
ℎ = 510
Hence, the height is 510 units
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I need to show you a pic of the question
The y-intercept and the x-intercept are the various points on the y and x axes where the graph cuts through.
In this our graph, there are interceptions at y = 0.4 and x = 0.3.
Thus, y-intercept exists at (0, 0.4) and x intercept at (0.3, 0)
I need help with Slopes!
we know that
To find out the slope of the line, we use the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]we need two points
Looking at the graph
we take the points
(1,3 ) and (2,5)
substitute in the formula above
[tex]\begin{gathered} m=\frac{5-3}{2-1} \\ m=\frac{2}{1} \\ m=2 \end{gathered}[/tex]therefore
the slope of the line is 2Jackie had 2 part time jobs at Shoney's Restaurant. One week she earned a total $306, working 12 hours as a cashier and 10 hours as a cook. The next week, sheworked 14 hours as a cashier and 22 hours as a cook, earning $512. How much doesshe earn per hour as a cashier?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the terms with a variable
Let x be the amount she earns per hour as a cashier
Let y be the amount she earns per hour as a cook
STEP 2: Interpret the statements in the question as seen below:
[tex]\begin{gathered} 12x+10y=306 \\ 14x+22y=512 \end{gathered}[/tex]STEP 3: Solve the simultaneous equation using elimination to get x and y
[tex]\begin{gathered} 12x+10y=306---(1) \\ 14x+22y=512----(2) \\ \\ \text{ Multiply equation 1 by 14 and equation 2 by 12} \\ 14\lbrack12x+10y=306\rbrack\Rightarrow168x+140y=4284----(3) \\ 12\lbrack14x+22y=512\Rightarrow168x+264y=6144----(4) \\ \\ \text{Subtract equation 4 from equation 3} \\ 168x\text{ cancels 168x, we have;} \\ 140y-264y=4284-6144 \\ -124y=-1860 \\ \text{Divide both sides by -124} \\ \frac{-124y}{-124}=\frac{-18600}{-124} \\ y=15 \end{gathered}[/tex]STEP 4: Solve any of equation to get the value of x
[tex]\begin{gathered} \text{From equation 1} \\ 12x+10y=306 \\ y=15\text{, By substitution;} \\ 12x+10(15)=306 \\ 12x+150=306 \\ \text{Subtract 150 from both sides} \\ 12x+150-150=306-150 \\ 12x=156 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{156}{12} \\ x=13 \end{gathered}[/tex]Since x represents the amount she earns as a cashier, hence She earns $13 per hour as a cashier
Question 2 of 5
Which of the following is not an expression?
A. + 1 = 4
B. 3 - 2x
C. 4x+7
D. x/3 - 1
Answer:
A.
Step-by-step explanation:
The answer is A, because an expression does not have an equal sign.
Opens down with compression coefficient of 0.2. Shifted right 1 unit and down 6 unitshow do I right this as a parabola equation?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
opens down
compression coefficient = 0.2
translated:
right 1
down 6
parabola equation = ?
Step 02:
opens down
(x - h)² = -4p (y - k)
compression coefficient = 0.2
0.2 (x - h)² = -4p (y - k)
translated:
right 1
down 6
0.2 (x - 1)² = -4p (y + 6)
The answer is:
0.2 (x - 1)² = -4p (y + 6)
Urgent!!! Long division
So, we know the bus can hold 20 people in 15 minutes, so the rate per hour is:
20/15m
60m/15m
4
20/15 x 4/4m
80/60m (80 per hour)
4/1 = 4
80/60m x 4/4
320/240m
320/4h
320 people could ride the bus in 4 hours.
find the difference between the mode and median of the distribution of data
Step 1: Rewrite the dot plot in tabular form
Step : Compute the mode
From the table, we can see that the numer appears most ( that is the number with the highest frequence, f) is 4.
Therefore,
mode = 4
Step 3: Find the median
First arrange the data in ascending order. In this case, the data is already in ascending order.
If ∑f is odd, the median is the middle value which is at position
[tex]\frac{\sum f+1}{2}[/tex]If ∑f is even, the median is the average of the two values at positions
[tex]\frac{\sum f}{2}\text{ and }\frac{\sum f}{2}+1[/tex]In this case, ∑f = 12 is even.
Therefore, the median is the average of the numbers at position 6 and 7
number at position 6 is 3
number at position 7 is 4
Hence, the median is given by
[tex]\frac{3+4}{2}=\frac{7}{2}=3.5[/tex]median = 3.5
Step 4: Find the difference between the median and mode
The difference is given by
[tex]4-3.5=0.5[/tex]Hence the difference is 0.5
8) Find the volume of a cylinder that has a radius of 9 cm and a height of 15 cm. 15 cm 9 cm
In order to find the volume of the given cylinder, use the following formula:
V = π·r²·h
where:
r: radius of the cylinder = 9 cm
h: height of the cylinder = 15 cm
π = 3.1415
replace the previous values of the parameters into the formula for V:
V = (3.1415)(9 cm)²(15 cm)
V = 3,816.92 cm³
Hence, the volume of the given cylinder is 3,816.92 cm³
use the ratio to solve , how can the table help me to solve ? how do I find part? please assist me
We have to determine te 30 percent of 50.
[tex]\frac{30}{100}\times50=15[/tex]Hence the answer is 15.
I would like to this math sentence question that I will send a picture of
Let
x -----> number of hours
we have that
the inequality that represents this situation is
[tex]45-12t\ge9[/tex]solve for t
[tex]\begin{gathered} -12t\ge9-45 \\ -12t\ge-36 \\ t\leq3 \end{gathered}[/tex]that means
the bakery can sell bread for a timeless than or equal to 3 hours
Part A: At a fair, Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times. Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times. Let x represent the number of tickets it takes to ride a roller coaster. Let y represent the number of tickets it takes to ride the bumper cars. Model Derrick and Javier's trip to the fair by creating linear equations to represent how Derrick and Javier each used their ride tickets. 4 X + y = Derrick: Javier: X + Blank 1: 4 Blank 2: Blank 3: Blank 4:
x: number of tickets it takes to ride a roller coaster
y: number of tickets it takes to ride the bumper cars
Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times, that is,
4x + 2y = 16
Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times, that is,
2x + 3y = 12
Graph the image of the figure on the right under the given translation.T(3,2)(x,y)
To translate the triangle we will translate each vertex using the rule of translation given
The vertice of the triangle are
(-1, 4), (-5, -2), (-8, 2)
The translation rule is T (3, 2)
That means we will add the x-coordinate of each point by 3,
and the y-coordinates by 2
The image of point (-1, 4) = (-1 + 3, 4 + 2) = (2, 6)
The image of point (-5, -2) = (-5 + 3, -2 + 2) = (-2, 0)
The image of point (-8, 2) = (-8 + 3, 2 + 2) = (-5, 4)
That means the triangle will move 3 units right and 2 units up
The images of the vertices are (2, 6), (-2, 0), (-5, 4)
Innings in his latest game,
The equation for the expression is given by
[tex]x+6\frac{2}{3}>82\frac{1}{3}[/tex]To get the value for x
Step 1: Subtract
[tex]\begin{gathered} 6\frac{2}{3} \\ \text{from both sides} \end{gathered}[/tex][tex]x+6\frac{2}{3}-6\frac{2}{3}>82\frac{1}{3}-6\frac{2}{3}[/tex][tex]x>82\frac{1}{3}-6\frac{2}{3}[/tex][tex]\begin{gathered} 82\frac{1}{3}=\frac{247}{3} \\ \\ 6\frac{2}{3}=\frac{20}{3} \\ \\ x>\frac{247}{3}-\frac{20}{3} \end{gathered}[/tex]Simplifying further
[tex]\begin{gathered} x>\frac{247-20}{3} \\ \\ x>\frac{227}{3} \end{gathered}[/tex][tex]\begin{gathered} x>\frac{227}{3}\text{ } \\ or \\ x>75\frac{2}{3} \end{gathered}[/tex]identify which value is not in the domain of the piecewise function
From the graph we notice that the only value of x for which the fuction generating the graph it not defined is x=-3.
Answer: A).
