so, we have the denominators of 4 and 8, thus our LCD will just be 8, but let's firstly convert the mixed fractions to improper fractions and find their difference.
[tex]\bf \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}}~\hfill \stackrel{mixed}{1\frac{7}{8}}\implies \cfrac{1\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{15}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{11}{4}-\cfrac{15}{8}\implies \stackrel{\textit{using LCD of 8}}{\cfrac{(2)11~~-~~(1)15}{8}}\implies \cfrac{22-15}{8}\implies \cfrac{7}{8}[/tex]
In the sum of two numbers is 15 and the product is 56, what are the two numbers?
ANSWER:
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Find the difference between the fastest girls time and the slowest girl time. Barbra ran 3 3/10, Donna ran 2 4/5 , Cindy ran 4 3/5 and Nicole ran 2 1/10
Answer: 2.5 or 2 1/2
Step-by-step explanation:
You can convert the mixed fractions to decimal numbers:
- Divide the numerator by the denominator of the fraction.
- Add the result to the whole number.
Thenyou have:
Barbara's time: [tex]3\ 3/10=3+0.3=3.3[/tex]
Donna's time: [tex]2\ 4/5=2+0.8=2.8[/tex]
Cindy's time: [tex]4\ 3/5=4+0.6=4.6[/tex]
Nicole's time: [tex]2\ 1/10=2+0.1=2.1[/tex]
As you can see, the fastest girl is Cindy and the slowest girl is Nicole.
Then, you must make the following subtraction to calculate the difference:
[tex]4.6-2.1=2.5[/tex] or 2 1/2
Answer:
Cindy's correct time is 3 2/5 (for the portfolio assignment that this question goes with).
Step-by-step explanation:
In Amy's garden the ratio of herbs to plants is 5:2. If there are 40 herb plants, how many vegetable plants are in her garden?
Hayden bought 48 new trading cards.Three fourths of the new cards are baseball cards.How many baseball cards did hayden buy?
Answer:
36
Step-by-step explanation:
1. 48 divided by 3= 12
2. 12 x 3= 36
(17.33) A randomized comparative experiment examined the effect of a technique for improving one’s ability to focus one’s attention on performance of undergraduate students on the Verbal portion of the Graduate Record Exam (GRE). The researchers found a statistically significant improvement in performance on the Verbal GRE (P = 0.05). When asked to explain the meaning of (P =0.05) a student says, “This means there is only probability equal to 0.05 that the null hypothesis is true.” Explain what P= 0.05 really means in a way that makes it clear that the student's explanation is wrong. P = 0.05 means that the outcome is at least 5% higher among one group than among the other group. P = 0.05 means that there is a probability of 0.05 that the null hypothesis is false. P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05. P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is less than 0.05.
Answer:
See below
Step-by-step explanation:
What the significance level tells us is that, in this case, there is only a 5% chance that the change in results from the sample happened by random chance. So that means that most likely the change in results did not happen by random change, and something happen between the times the samples were taken. In this case, the experiment.
P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05.
P = 0.05 does not represent the probability that the null hypothesis is true or false, nor does it signify that the outcome is 5% higher in one group compared to the other. Instead, P = 0.05 is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as the one observed. In simpler terms, it indicates the likelihood of obtaining the observed results, or results more extreme, under the assumption that there is no true effect or difference between the groups.
In hypothesis testing, researchers start with a null hypothesis (H0) that states there is no effect or difference between the groups being compared. The alternative hypothesis (Ha), on the other hand, posits that there is a significant effect or difference. The p-value quantifies the strength of evidence against the null hypothesis. A low p-value (such as P = 0.05) suggests that the observed results are unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.
When a study reports a statistically significant improvement in Verbal GRE performance with P = 0.05, it means that the probability of obtaining the observed improvement (or a more significant one) under the assumption of no actual effect is 5% or less. Therefore, there is strong evidence to suggest that the technique used in the experiment does indeed have a positive impact on students' Verbal GRE scores.
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Use the figure below to find the Measure of Angle BEH
Explain/Show how you got your answer please
Answer:
The answer is ; m∠BEH = 55°
Step-by-step explanation:
Twice Jack's age plus 5 is 21. Write and solve an equation. How old is Jack? A) 8 B) 13 C) 32 D) 52
Answer:
A - 8
Step-by-step explanation:
(21-5)/2
16/2 = 8
Answer: Jack is 8 years old (option A)
Step-by-step explanation:
Hi, to answer this question we have to write an equation using the information given:
Twice Jack's age plus 5 is 21Twice : Means that the age of jack (j) is multiplied by 2 (2j),
Plus 5: we have to add 5 (2j+5).
Is 21: all is equal to 21.
Mathematically speaking:
2j +5 =21
Solving:
2j =21-5
2j =16
j= 16/2
j=8
Option A). 8
Feel free to ask for more if needed or if you did not understand something.
A shoe store is selling a pair of shoes for $60 that has been discounted by 20%. What was the original selling price? Show your work.
Answer:
The original selling price was [tex]\$75[/tex]
Step-by-step explanation:
Let
x-----> the original selling price
we know that
[tex]100\%-20\%=80\%=80/100=0.80[/tex]
so
[tex]0.80(x)=60[/tex] -----> equation that represent the situation
solve for x
Divide by 0.80 both sides
[tex]x=60/0.80=\$75[/tex]
A circle is divided into 9 equal parts. What is the angle measured of two of those parts?What is the degrees
Answer:
Angle of 1 part: 40°
Angle of 2 parts: 80°
Step-by-step explanation:
Angles in a circle / Equal parts of a circles = Angle of 1 part
360/9 = 40°
40 x 2 = 80
Please help me with this problem
Diagonal = SQRT(8^2 + 12^2 + 30^2)
Diagonal = SQRT(64 + 144 + 900)
Diagonal = SQRT(1108)
Diagonal = 33.3 feet
Factorise 36x - 16 please :)
Answer:
4(9x-4)
Step-by-step explanation:
➷ Find the greatest common factor between the two values:
In this case, it is 4
This value will go outside the parenthesis
Divide each of the values by 4:
36x/4 = 9x
-16/4 = -4
The final answer is 4(9x - 4)
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A student needs to collects at least 10 flowers for a science project the student has already collected 3 flowers the inequality shown can be useed to find n the number of flowers the student still needs
he is still looking for seven more flowers
Answer:
The answer is n, greater than or less than 13.
The sum of two numbers is 16 and their difference is 20. What are the two numbers?
Final answer:
To find the two numbers whose sum is 16 and difference is 20, we set up two equations from the given conditions and solve them simultaneously, yielding the numbers 18 and -2.
Explanation:
The student has asked about solving a system of equations where the sum of two numbers is 16 and their difference is 20. We can set up two equations based on the given information:
x + y = 16 (Equation 1, where x and y are the two numbers)
x - y = 20 (Equation 2, because the difference between the two numbers is 20)
To find the two numbers, we can solve this system of equations by adding both equations to eliminate the 'y' variable:
2x = 36
Dividing both sides by 2 gives us x = 18. We then substitute x back into Equation 1 to find y:
18 + y = 16 => y = 16 - 18 => y = -2
Therefore, the two numbers are 18 and -2.
Consider that the length of rectangle A is 10 cm and its width is 6 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 6 cm. B) A rectangle with a length of 15 cm and a width of 9 cm. C) A rectangle with a length of 14 cm and a width of 7 cm. D) A rectangle with a length of 12 cm and a width of 8 cm.
Lata has collected 75 pennies. Lata's father says that if she arranges the pennies in 15 rows, Lata will be able to make a rectangle using all of her pennies. Is her father correct?
Answer:
Yes - he is correct
Step-by-step explanation:
If she has 75 pennies, she would have 15 rows with 5 pennies in each row with a 3:5 ratio for the rectangle.
Lata's father is correct.
What is a rectangle?Rectangle is a type of quadrilateral having two opposite sides that are equal in measurement.All the angles of Rectangle are of 90°.
Area of rectangle = Length * Width
Perimeter of rectangle =2(length + width)
Given,
Total number of pennies Lata have = 75
If she arranges the pennies in 15 rows with 5 pennies in each row.
i.e; 15 * 5 = 75
Then she will get Rectangle of side of length 15 and width 5
So, her father is correct.
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Help with this question, please ASAP!!
Answer:
[tex]\large\boxed{P=(16+36x)\ ft}[/tex]
Step-by-step explanation:
The formula of an area of a rectangle:
[tex]A=bh[/tex]
b - base
h - height
We have A = 144x ft² and h = 8. Substitute and solve for b:
[tex]144x=8b[/tex] divide both sides by 8
[tex]b=18x\ ft[/tex]
The formula of a perimeter of a rectangle:
[tex]P=2b+2h[/tex]
Substitute:
[tex]P=2(18x)+2(8)=36x+16[/tex]
Jack’s favorite colors are blue and red.
He has 2 blue shirts, 1 red shirt, 1 blue jacket, 1 red belt, 1 blue pair of pants and 1 red pair of pants.
Jack selects one of these garments at random. Let A be the event that he selects a blue garment and B be the event that he chooses a belt.
What is the probability that the garment Jack chooses is either blue or a belt?
Answer:
5/7 or 71%
Step-by-step explanation:
4/7 (blue) + 1/7 (belt) = 5/7
Answer: Probability of event A = 0.57
Probability of event B = 0.14
Step-by-step explanation:
The data is:
2 blue shirts
1 red shirt
1 blue jacket
1 red belt
1 blue pair of pants
1 red pair of pants
the total number of garments is: 2 + 1 + 1 + 1 + 1 + 1 = 7
the number of blue ones is: 2 + 1 + 1 = 4
the number of belts is: 1
then, the probability of selecting at random one blue garment is equal to the number of blue ones divided the total number:
Pa = 4/7 =0.57
the probability of selecting the belt is equal to the number of belts divided the total number of garments, this is:
Pb = 1/7 = 0.14
Every year 39 million cars cross the Golden Gate Bridge in San Francisco. Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge, exponential or linear?
Answer:
Linear
Step-by-step explanation:
Hello
Is linear
Best regards
Answer:
Linear
Step-by-step explanation:
Linear function : if the value increases with the constant value per period,
It can written as y = a + bx
Where, a = initial value, b = constant value per period,
Exponential function : if the value increases with the constant rate per period,
It can be written as,
[tex]y=ab^x[/tex]
Where, a = initial value, b = growth factor per period.
∵ Every year 39 million cars cross the Golden Gate Bridge in San Francisco.
Then after x years, the number of cars ( in million )
f(x) = 39x
⇒ f(x) = 0 + 39x
By the above explanation,
Hence, the function that represents the number of cars that have crossed the Golden Gate Bridge is linear.
You estimate you can do 12 math problems in 45 minutes. How long should it take you to do 20 math problems?
[tex]\bf \begin{array}{ccll} problems&minutes\\ \cline{1-2} 12&45\\ 20&x \end{array}\implies \cfrac{12}{20}=\cfrac{45}{x}\implies \cfrac{3}{5}=\cfrac{45}{x}\implies 3x=225 \\\\\\ x=\cfrac{225}{3}\implies x=75[/tex]
It takes 75 minutes to solve 20 math problems.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here it takes 45 minutes to solve 12 math problems thus to solve 1 math problem it will take t= 45/12
=3.75 minutes
Thus to solve 20 math problems it will take t₂₀=3.75×20
=75 minutes
Hence, It takes 75 minutes to solve 20 math problems.
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A factory makes boxes with length to width ratio of 6 inches to 1 inch. What should be the width of a box with a length of 30 inches
Length:width
6 inches: 1 inch
30 inches: 5 inches
Since the ratio for length is multiplied by 5, you would do the same for width.
Jimmy is planning to paint the gate of his house. The gate has a glass panel. Painting the gate costs $2.50 per square foot. How much will he have to spend to paint the gate? PLEASE HELP!!
Answer: Third option.
Step-by-step explanation:
Calculate the area of the gate (including the glass panel) which has the shape of a trapezoid.
The formula for calculate the area of a trapezoid is:
[tex]A=\frac{h}{2}(B+b)[/tex]
Where h is the height, B is the larger base and b is the smaller base.
In this case:
[tex]B=10ft\\b=7ft\\h=5ft[/tex]
Substituting, you get:
[tex]A_{gate}=\frac{5ft}{2}(10ft+7ft)=42.5ft^2[/tex]
Calculate the area of the rectangular glass panel, with the formula:
[tex]A_{panel}=l*w[/tex]
Where the lenght is [tex]l=1.43ft[/tex] and the width is [tex]w=0.71ft[/tex]
Then:
[tex]A_{panel}=(1.43ft)(0.71ft)=1.01ft^2[/tex]
The area he needs to paint is:
[tex]A=A_{gate}-A_{panel}\\A=42.5ft^2-1.01ft^2\\A=41.49ft^2[/tex]
If painting the gate costs $2.50 per ft², for 41.49 ft² he will have to spend:
[tex]=(41.49)(\$2.50)\\=\$103.725[/tex]
Therefore the answer is the third option.
To calculate the cost of painting the gate, find the area of the glass panel by multiplying its length and width. Multiply the area by the cost per square foot to find the total cost.
Explanation:To calculate the cost of painting the gate, we need to find the area of the glass panel first. Let's say the length of the panel is 'l' feet and the width is 'w' feet. The area of a rectangle is given by the formula A = l × w. Once we have the area, we can multiply it by the cost per square foot ($2.50) to find the total cost. So the formula to calculate the cost of painting the gate is: Cost = Area × Cost per square foot. Substitute the values you know into the formula and solve for the cost.
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Please help! Will give the brain thing! 40 points.
Simplify each Polynomial Expression:
1. 2x(-3x - 1)
2. -x(4 + 2x)
3. -5x(-2x + 4)
4. x(-2x - 2) + 3(-4x - 6x)
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
Answer:
1. 2x(-3x - 1)
-6x^2 - 2x
2. -x(4 + 2x)
-4x - 2x^2
3. -5x(-2x + 4)
10x^2 - 20x
4. x(-2x - 2) + 3(-4x - 6x)
-2x^2 - 2x - 12x - 18x
-2x^2 - 32x
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
-6x^2y - 10xy^2 -8xy^2 - 16yx
-6x^2y -18xy^2 - 16yx
You just distribute (multiply) what's outside the parentheses with everything inside the parentheses. Then, combine like terms.
Answer:
1. 2x(-3x - 1)
-6x^2 - 2x
2. -x(4 + 2x)
-4x - 2x^2
3. -5x(-2x + 4)
10x^2 - 20x
4. x(-2x - 2) + 3(-4x - 6x)
-2x^2 - 2x - 12x - 18x
-2x^2 - 32x
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
-6x^2y - 10xy^2 -8xy^2 - 16yx
-6x^2y -18xy^2 - 16yx
Solve for x ... x/6 = 2
Answer:The answer is x=12
Step-by-step explanation: 2*6=12 and 12/6=2
Answer:
x = 12
Step-by-step explanation:
12/6 = 2
A triangle has a perimeter of 206 inches. if the two sides of the triangle measure 59 inches and 94 inches, determined the length of other side.
➷ The perimeter is the sum of all the lengths
206 - (59 + 94) = 53
It is 53 inches.
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Answer:
53 inches.
Step-by-step explanation:
Perimeter = sum of the 3 sides so the third side
= 206 - 94 - 59 = 53.
The equation of the line of best fit of a scatter plot is y = −5x − 2. What is the slope of the equation?
Answer:
SLOPE = -5
Step-by-step explanation:
Because that's what x is.
A certain organization recommends the use of passwords with the following format: vowel commavowel, consonant comma consonant comma consonant comma vowel comma consonant comma number comma numberconsonant, consonant, consonant, vowel, consonant, number, number (for example, inpray 93inpray93). Assume that repeats are allowed. Complete parts (a) and (b). (a) Assuming passwords are not case sensitive, how many such passwords are possible (assume that there are 5 vowels and 21 consonants)?
The password format is = inpray93
vowel , consonant, consonant, consonant, vowel, consonant, number, number.
There are 21 consonants, 5 vowels and 10 number choices (0-9)
Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices are available and for 7th and 8th position there are 10 choices (0 to 9).
Passwords are not case sensitive which means upper case and lower case letters are same.
So, the number of passwords can be =
[tex]5\times21\times21\times21\times5\times21\times10\times10[/tex]
= 486202500
Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.
This means all the letters are different.
So, number of passwords will be =
[tex]10\times42\times42\times42\times10\times42\times10\times10[/tex]
= 31116960000
What is the measure of EFG?
Answer: [tex]149^{\circ}[/tex]
Step-by-step explanation:
From the given figure, the measure of central angle FDG is given by :-
[tex]\angle{EDG}=\angle{EDF}+\angle{FDG}\\\\=83^{\circ}+66^{\circ}\\\\=149^{\circ}[/tex]
We know that the measure of arc in degrees is equals the measure of the central angle that intercepts the arc.
Now,the measure of arc EFG is given by :-
[tex]Arc\ \text{EFG}=\text{Central angle EDG}=149^{\circ}[/tex]
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you'll be a magic elf?
Answer:
1/15
Step-by-step explanation:
You have a 1/3 chance of being an elf.
You have a 1/5 change of having the magic tool.
1/3 × 1/5 = 1×1/3×5 = 1/15
Answer:
it is 1/15
Step-by-step explanation:
Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points for each visit to the movie theatre. - He needs at least 55 points to earn a free movie ticket. Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his firs free movie ticket?
A 3.5x+15≥553.5x+15\ge553.5x+15≥55
B 3.5+15x≥553.5+15x\ge553.5+15x≥55
C 3.5+15x ≤ 553.5+15x\ \le\ 553.5+15x ≤ 55
D 3.5x+15 ≤ 553.5x+15\ \le\ 553.5x+15 ≤ 55
Answer:
Option A. 3.5x + 15 ≥ 55
Step-by-step explanation:
Points Rosh received for becoming a member = 15
Points Rosh received for visiting the moving theater = 3.5
Total points needed for a free movie ticket = 55
For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.
Total points = Points received on becoming a member + Points received on x visits
So,
Total Points = 15 + 3.5x
These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:
3.5x + 15 ≥ 55
So, option A gives the correct answer
Answer:
option. A
Step-by-step explanation:
I had the exacgt same question
Formulate the quadratic function that contains the points (-1,2), (0,-1) and (2,5).
1.) f(x) = 2x^2 + x + 1
2.) f(x) = 2x^2 - x - 1
3.) f(x) = 2x^2 - x + 2
4.) f(x) = 2x^2 - x - 2
Answer:
option 2
2x²- x - 1
Step-by-step explanation:
We are given points: (-1,2), (0,-1) and (2,5)
Substitute each point one by one in the quadratic equation to check if the quadratic equation contains all points mention.
2) f(x) = 2x²- x - 1
Point(-1,2)
f(-1) = 2(-1)² -(-1) -1
2 = 2 + 1 - 1
2 = 2
Point(0,-1)
f(0) = 2(0)² -(0) -1
-1 = 0 - 0 -1
-1 = -1
Point(2,5)
f(2) = 2(2)² -(2) -1
5 = 8 - 2 -1
5 = 6 - 1
5 = 5