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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(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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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.
Find the value of x and the value of y.
This would be D cause these are 30,60, 90 angles. 30 (X) 60(X square root of 3 and 90 2x).
Answer:
C
Step-by-step explanation:
Using the sine ratio on the right triangle on the right side
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex]
Multiply both sides by 8 × sin30° = y
⇒ y = 8 × [tex]\frac{1}{2}[/tex] = 4 → C
For questions 4-5, how many solutions does the system have?
4. -4y+4=x
2x+8y=8
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution
5. 6x+2=y
3y-18x=12
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution
Answer:
[tex]\large\boxed{Q4.\ C.\ \text{Infinitely Many Solutions}}\\\boxed{Q5.\ D.\ \text{No Solution}}[/tex]
Step-by-step explanation:
[tex]Q4.\\\\\left\{\begin{array}{ccc}-4y+4=x&(1)\\2x+8y=8&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(-4y+4)+8y=8\qquad\text{divide both sides by 2}\\-4y+4+4y=4\qquad\text{combine like terms}\\4=4\qquad\bold{TRUE}\\\\\text{Infinitely Many Solutions}[/tex]
[tex]Q5.\\\\\left\{\begin{array}{ccc}6x+2=y&(1)\\3y-18x=12&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3(6x+2)-18x=12\qquad\text{divide both sides by 3}\\6x+2-6x=4\qquad\text{combine like terms}\\2=4\qquad\bold{FALSE}\\\\\text{No Solution}[/tex]
What is the value of x in the equation 3(2x + 4) = ?6? (4 points) ?3 1 12 19
Answer:
2
Step-by-step explanation:
3(2x + 4)=?
6x + 12
6x/6=x
12/6=2
x=2
The service time distribution describes the probability P that the service time of the customer will be no more than T hours. If m is the mean number of customers serviced in an hour, then P=1-e^mt
Answer: option d.
Step-by-step explanation:
You have the following formul given in the problem:
[tex]p=1-e^{-mt}[/tex]
You know that:
The number of customers serviced in an hour by the technical support representative is 6 costumbers, therefore:
[tex]m=6[/tex]
As the problem asked for the probability that a costumber will be on hold less than 30 minutes, we know that:
[tex]t=0.5[/tex]
Substitute the values above into the formula.
Then, you obtain:
[tex]p=1-e^{-(6)(0.5)}=0.95[/tex] or 95%
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
When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10
Final answer:
The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses and simplify. Then, solve for x by isolating the variable.
Explanation:
The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses. This can be done by multiplying -2 with each term inside the parentheses.
So, -2(x+3) becomes -2x-6. The equation now becomes -2x - 6 = -10.
Now, we can proceed with solving the equation by isolating the variable x.
We can begin by adding 6 to both sides of the equation to get -2x = -4.
Finally, we divide both sides of the equation by -2 to solve for x.
So, x = 2.
The correct answer is option c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]
When solving the equation -2(x+3)=-10, the best first step is to divide both sides by 2. This simplifies the equation by making it easier to solve.
Here are the steps:
Divide both sides by 2: [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]Equation simplifies to: -(x+3) = -5Open parantheses: -x-3 = -5Rearrange: x = 5-3 = 2By dividing first, you simplify the algebraic manipulation and make solving the equation straightforward.
The complete question is:
When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10
a. [tex](-2)(-2)(x+3) = -10(-2)[/tex]
b. [tex]\frac{-1}{\ 2}(-2)(x+3) = (-10)\frac{-1}{\ 2}[/tex]
c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]
d. [tex]\frac{-2}{-10}(x+3) = \frac{-10}{-10}[/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:
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.
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
Later 7 students joined group 2 (41 students)and one student left to join group 1. (44 students) Now 20 students play trombone and 7 more students play trumpet as play saxophone. How many students play each instrument?
48 students in group 2
43 students in group 1
So in total there are 91 students
7 students play the trump
And 20 play the trombone
Therefore it is known that 27 students play those two instruments in total
Because of this, Subtract 27 from 91 to get the num of students who doesn't play those instruments.
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.
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
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?
Mark and Henry win some money and share it in the ratio 1:3. Mark gets ?9. How much did Henry get?
Evaluate the log.
[tex]log\frac{1}{27} 81[/tex]
Answer:
−115.940465
Step-by-step explanation:
Simplified = −115.940465
Answer:
-4/3.
Step-by-step explanation:
Using the change of base formula convert to log 3:
logb x = loga x / loga b
log(1/27) 81 = log3 81 / log3 1/27
log3 81 = 4 ( because 3^4 = 81) and log3 1/27 = -3 (because 3^-3 = 1/27)
So log(1/27) 81 = 4/-3 = -4/3.
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
Third-grade students at washington School read 530 books in march.They read 469 books in April.How many books did they read in the two months?
Answer:
999
530
+469
----------
999
If two angles form a linear pair and the m<1 =2x + 20 and m< 2 = 48x, find the measure of each angle
Answer:
[tex]m<1=26.4\°[/tex]
[tex]m<2=153.6\°[/tex]
Step-by-step explanation:
we know that
If m<1 and m<2 form a linear pair
then
[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles
substitute the values and solve for x
[tex](2x+20)+48x=180\°[/tex]
[tex]50x=180\°-20\°[/tex]
[tex]50x=160\°[/tex]
[tex]x=3.2\°[/tex]
Find the measure of each angle
[tex]m<1=(2x+20)=2(3.2\°)+20\°=26.4\°[/tex]
[tex]m<2=48x=48(3.2\°)=153.6\°[/tex]
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.
Can anyone please help me!? Help!
Subject: Expanding and Simplifying Expressions
7th-grade Mathematics!
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Question #1: Write an expression that is equivalent to 2/3 (4x + 9).
A) 8/3x + 6
B) 8/3x + 9
C) 2/3x + 6
D) 2/3x + 9
-------------------------------------------------------------------------------------
Question #2: Which expression is equivalent to 1/3p + 15?
A) 1/3(p + 45)
B) 1/3(p + 5)
C) 3(p + 45)
D) 3(p + 5)
Answer:
[tex]\large\boxed{Q\#1.\ A)\ \dfrac{8}{3}x+6}\\\boxed{Q\#2.\ A)\ \dfrac{1}{3}(p+45)}[/tex]
Step-by-step explanation:
[tex]Q\#1:\\\\\dfrac{2}{3}(4x+9)\qquad\text{use the distributive property}\\\\=\left(\dfrac{2}{3}\right)(4x)+\left(\dfrac{2}{3}\right)(9)=\dfrac{8}{3}x+(2)(3)=\dfrac{8}{3}x+6\\\\Q\#2:\\\\\dfrac{1}{3}p+15=\dfrac{1}{3}p+\dfrac{1}{3}\cdot(3)(15)=\dfrac{1}{3}p+\dfrac{1}{3}\cdot45=\dfrac{1}{3}(p+45)[/tex]
My sister is 14 years old my brother says that his age minus 12 is equal to my sisters age how old is my brother
Answer:
26
Step-by-step explanation:
Let his age = x
Equation
x - 12 = 14
Solution
Add 12 to both sides.
x - 12 +12 = 14 + 12
x = 26
He is currently 26 years old.
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]
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.
If 50 is increased by 40%, what is the new amount?
Answer:
70
Step-by-step explanation:
50+20 = 70
ANSWER
70
EXPLANATION
We want to increase 50 by 40%
Method 1
New amount =50+40% of 50
[tex] = 50 + \frac{40}{100} \times 50[/tex]
[tex] = 50 + \frac{40}{2} [/tex]
[tex] = 50 + 20[/tex]
[tex] = 70[/tex]
Method 2.
50 corresponds to 100%.
New amount corresponds to (100+40=140)%
This implies that, New amount
[tex] = 140\% \times 50[/tex]
[tex] = \frac{140}{100} \times 50[/tex]
[tex] = \frac{140}{2} [/tex]
[tex] = 70[/tex]
For which equation would x = 5 be a solution?
4x - 7 = 27
3x + 6 = 21
12 - 2x = 13
7 + 6x = 27
Answer:
The second option.
3x + 6 = 21.
Step-by-step explanation:
3x + 6 = 21.
If x = 5, plug it in.
3 · 5 + 6 = 21
15 + 6 = 21
Hope this helps,
Davinia.
Answer:
Second Option
Step-by-step explanation:
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.
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.