Answer:
A.
Step-by-step explanation:
The visual representation is All integers are also rational numbers
what are rational number?A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.
So, we have sets of real number.
As. we know
All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.
Hence, integers are also rational numbers
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solve the equation by using the quadratic formula. x^2+2x=6
Answer:
[tex]\Huge \boxed{{x=-1\pm \sqrt{7}}}[/tex]
Step-by-step explanation:
x² + 2x = 6
Subtract both sides by 6.
x² + 2x - 6 = 0
ax²+bx+c=0
a=1, b=2, and c=-6
We can apply the quadratic formula.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Plug in the values.
[tex]\displaystyle x=\frac{-2\pm\sqrt{2^2-4(1)(-6)}}{2(1)}[/tex]
Evaluate.
[tex]\displaystyle x=\frac{-2\pm\sqrt{4-(-24)}}{2}[/tex]
[tex]\displaystyle x=\frac{-2\pm\sqrt{28}}{2}[/tex]
[tex]\displaystyle x=\frac{-2\pm 2\sqrt{7}}{2}=-1 \pm \sqrt{7}[/tex]
Answer: Edmentum and Plato
Step-by-step explanation:
730,000,000 in scientific notation.
Answer:
7.3×10^8
Step-by-step explanation:
Hi
scientific notation mean the answer is of the form x *10^y
where x ∈ [1; 10[ and y ∈ Z
so 730 000 000 is 7.3 * 10^8
Evaluate the expression, when y = 2.
4y - 6 + 5y = y
Answer:
12
Step-by-step explanation:
4y - 6 + 5y = y
place 2 in the spot of y
4(2) - 6 + 5(2)= y
keep that last y the way it is
4•2=8 5•2=10
8-6+10=y
Simplify
2+10=y
12=y
Question Details
Find the distance between X(-3, 8) and Y (6, -6).
Round answer to the nearest tenth. Pls show work
Answer:
16.64
Step-by-step explanation:
Distance between any two points (x1,y1) and (x2,y2) is given by
Distance = [tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]
Given point
X(-3, 8) and Y (6, -6).
The distance XY will be
[tex]XY = \sqrt{(-3-6)^{2} + (8 - (-6)^{2} }\\XY = \sqrt{(-9)^{2} + (8 +6)^{2} }\\XY = \sqrt{81 + 196 }\\XY = \sqrt{277 }\\XY = 16.64[/tex]
Thus, distance between X(-3, 8) and Y (6, -6) is 16.64 , rounded to nearest tenth.
Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨2,−3,4⟩, b=⟨−4,5,−1⟩, and c=⟨−2,−1,5⟩.
Answer:
derivative of the vector function given = ( -16-22t, 14-36t, -2-16t )
Step-by-step explanation:
given data:
vector function : r(t) = ta*(b+tc)
a = ( 2,-3.4) . b = (-4,5,-1). c = ( -2,-1,5)
to find the derivative of the vector function we will differentiate with respect to x attached below is the detailed solution
The cafeteria sells each apple at one price and each banana at another price. For 5 apples and 3 bananas Dan pays $5.70. For 3 apples and 5 bananas Chris pays $4.70. The price of one apple is how much more then the price of one banana, in cents?
Answer:
50
Step-by-step explanation:
a = # of apples
b = # of bananas
5a + 3b = 570
3a + 5b = 470
Solve with substitution or elimination. To solve by elimination, multiply the first equation by 5 and the second equation by 3.
25a + 15b = 2850
9a + 15b = 1410
Subtract:
16a = 1440
a = 90
Plug into either equation to find b.
5(90) + 3b = 570
450 + 3b = 570
3b = 120
b = 40
So apples are 90 cents, and bananas are 40 cents. Therefore, apples are 50 cents more than bananas.
Domain: The set of all states Range: The set of all senators (Remember, each state has two senators!) This relation is ✔ not a function . Create your own real-world example of a relation that is a function. Domain: The set of
Answer:
Not a function
Step-by-step explanation:
A kayaker moves 32 meters northward, then 6 meters
southward, and finally 16 meters northward.
For this motion, what is the distance moved?
Answer:
distance moved by kayaker is 54m
Which Excel function will give the p-value for overall significance if a regression has 75 observations and 5 predictors and gives an F test statistic Fcalc = 3.67?
Answer:
The excel function that will gibe the p-valur for overall significance of a regression has 75 observations and 5 predictors and gives an F test statistic FCal = 3.67 is given below:
F.DIST.RT(3.67,5.69)
Two hoses are filling a pool the first hose fills at a rate of x gallons per minute the second hose fills at a rate of 15 gallons per minute less than the first hose.
Answer:
B. (0, 5]∪(15,30] only (15,30] contains viable rates for the hoses.
Step-by-step explanation:
The question is incomplete. Find the complete question in the comment section.
For us to meet the pool maintenance company's schedule, the pool needs to fill at a combined
rate of at least 10 gallons per minute. If the inequality represents the combined rates of the hoses is 1/x+1/x-15≥10 we are to find all solutions to the inequality and identifies which interval(s) contain viable filling rates for the hoses. On simplifying the equation;
[tex]\frac{1}{x} + \frac{1}{x-15} \geq \frac{1}{10}\\\\ find\ the \ LCM \ of \ the function \ on \ the \ LHS\\\\\frac{x-15+x}{x(x-15)} \geq \frac{1}{10}\\\\\frac{2x-15}{x(x-15)} \geq \frac{1}{10}\\\\10(2x-15)\geq x(x-15)\\\\20x-150\geq x^2-15x\\\\collect \ like \ terms\\-x^2+20x+15x - 150\geq 0\\[/tex]
[tex]-x^2+35x-150 \geq 0\\\\multipply \ through \ by \ minus\\x^2-35x+150 \leq 0\\\\(x^2-5x)-(30x+150) \leq 0\\\\x(x-5)-30(x-5) \leq 0\\\\[/tex]
[tex](x-5)(x-30) \leq 0\\\\x-5 \leq 0 and x - 30 \leq 0\\\\x \leq 5 \ and \ x \leq 30[/tex]
The interval contains all viable rate are values of x that are less than 30. The range of interval is (0, 5]∪(15,30]. Since the pool needs to fill at a combined rate of at least 10 gallons per minute for the pool to meet the company's schedule, this means that the range of value of gallon must be more than 10, hence (15, 30] is the interval that contains the viable rates for the hoses.
Please help ASAP!!! Plweaseeeeeeeeeeeeeeeeee
Answer:
A
Step-by-step explanation:
All of the following are rational numbers except
-16
1.33
2/3
3.14159...
Answer:
3.14159
Step-by-step explanation:
This number is pi. Pi goes on for millions of digits on end.
Answer:
The answer is pi. Pi goes on forever and irrational nunbers go on forever.
which is equivalent to the expression shown below
Step-by-step explanation:
-2a4 - 3a2 + 7a + 6 - 6a3 + a4 + 7a2 - 6
Solving like terms
-a4 - 6a3 + 4a2 + 7a
Option A is the correct answer
The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds can be modeled by the graph below. Which equation is represented in the graph below? On a coordinate plane, a curve crosses the y-axis at (0, negative 5). It increases to (1, 5) and then decreases to (2, negative 5). 5 cycles are shown.
The travel of the spring is it’s amplitude, which is a cosine function.
The lowest y value is -5
Multiply that by cosine of pi x time
The formula is d = -5cos(pi t)
The equation d = -5cos(πt) modeled the distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t.
We know the cosine equation for distance d:
d = acos(bt+c) + d
From the graph: a = -5, b = π
Assume the phase and vertical shift are zero.
c = 0 and d = 0
Plug all values in the function, the equation becomes:
d = -5cos(πt)
Thus, the equation d = -5cos(πt) modeled the distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds.
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The Laurier Company’s brand has a market share of 30%. Suppose that 1,000 consumers of the product are asked in a survey which brand they prefer. What is the probability that more than 32% of the respondents say they prefer the Laurier brand?
Answer:
The probability is
[tex]P(Z>1.3793 ) = 0.083901[/tex]
Step-by-step explanation:
From the question we are told that
The proportion proportion is [tex]p = 0.30[/tex]
The sample size is [tex]n = 1000[/tex]
The sample proportion [tex]\r p = 0.32[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{p (1 - p)}{ n} }[/tex]
[tex]SE = \sqrt{\frac{ 0.30 (1 - 0.30 )}{ 1000} }[/tex]
[tex]SE = 0.0145[/tex]
The probability that more than 32% of the respondents say they prefer the Laurier brand is mathematically represented as
[tex]P(X > 0.32 ) = P( \frac{X - p }{ SE} > \frac{\r p - p }{ SE} )[/tex]
Here [tex]\frac{X - p }{SE} = Z (the \ standardized \ value \ of \ X)[/tex]
[tex]P(X > 0.32 ) = P(Z>1.3793 )[/tex]
From the z -table [tex]P(X > 0.32 ) = P(Z>1.3793 ) = 0.083901[/tex]
[tex]P(Z>1.3793 ) = 0.083901[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a 0.0838 = 8.38% probability that more than 32% of the respondents say they prefer the Laurier brand.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex].In this problem:
The Laurier Company’s brand has a market share of 30%, hence [tex]p = 0.3[/tex]1,000 consumers are asked, hence [tex]n = 1000[/tex].Then, the mean and the standard error are given by:
[tex]\mu = p = 0.3[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.3(0.7)}{1000}} = 0.0145[/tex]
The probability that more than 32% of the respondents say they prefer the Laurier brand is 1 subtracted by the p-value of Z when X = 0.32, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.32 - 0.3}{0.0145}[/tex]
[tex]Z = 1.38[/tex]
[tex]Z = 1.38[/tex] has a p-value of 0.9162.
1 - 0.9162 = 0.0838
0.0838 = 8.38% probability that more than 32% of the respondents say they prefer the Laurier brand.
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A student is growing two plants for a science experiment. Each plant was a different height at the start of the experiment. Plant A was given only water and plant B was given water and food. The system of equations show how the heights of the plants, y, in inches have change over x weeks. Plant A: y = 8 + ½ x Plant B: y = 4 + (5/4) x
Answer:
A: 12.5 per week B= 12.75
Step-by-step explanation:
1/2 times 7 (days in a week) is 3.5. So A is 8+3.5=12.5. 7 times 5/4 is 8.75. So B is 4+8.75=12.75
A tap leaks at the rate of 2cm³ per second.How long will it take the tap to fill a container of 45litres capacity.
Answer:
6 hours 15 minutes
Step-by-step explanation:
1 litre = 1000cm³
45 litres = 45000cm³
Volume = rate × time
45000 = 2 × t
t = 22500 secs
= 375 mins
BRAINLIEST PLEASE
All time values listed above are equivalent, so you only need to pick one value to write as the answer.
======================================================
Work Shown:
1 liter = 1000 cubic cm
45 liters = 45*1000 = 45000 cubic cm
The container has a capacity of 45000 cubic cm
It will take 45000/2 = 22500 seconds to fill the container since the rate is 2 cubic cm per second.
-----------------
Convert from seconds to minutes
22500 seconds = (22500)*(1 min/60 sec)
22500 seconds = (22500/60) min
22500 seconds = 375 min
-----------------
Convert to hours
375 min = (375)*(1 hr/60 min)
375 min = (375/60) hr
375 min = 6.25 hr
----------------
Converting to hours,minutes
6.25 hr = 6 hr + 0.25 hr
6.25 hr = 6 hr + (0.25*60) min
6.25 hr = 6 hr + 15 min
6.25 hr = 6 hr, 15 min
2x+15=x/2-3
Can anyone solve for x?
Answer: X=-12
Right ain’t it ?
Can someone, please help me with this.
Step-by-step explanation:
Hope it helps u mate
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QUESTION 1 Evaluate −30 ÷ −6. a 5 b −5 c 6 d −6 QUESTION 2 Evaluate 62 ÷ (3 + 9). a3 b4 c12 d21 QUESTION 3 Danny made a mistake in the following problem. The mistake was made in Line . Only input the number of the first incorrect line. Line 1 21 + 35 ÷ 7 + 6(2) Line 2 21 + 5 + 6(2) Line 3 21 + 11(2) Line 4 21 + 22 Line 5 43
Answer:
A; ?; Line 3
Step-by-step explanation:
Question 1:
-30 divided by -6 is 5.
The negatives cancel each other out.
And 30 divided by 6 is simply 5.
Question 2:
[tex]62\div(3+9)[/tex]
Do the operation inside the parenthesis first:
[tex]62\div12[/tex]
Divide. 12 does not go into 62 evenly. 12 times 5 is 60, so the answer is 5 remainder 2:
[tex]62\div12=5\text { R}2[/tex]
Or in fractions:
[tex]31/6[/tex]
(Was there a typo? From what you've given me, the correct answer is not listed.)
Question 3:
So we have to following steps:
[tex]\text{Line 1: } 21+35\div7+6(2)\\\text{Line 2: }21+5+6(2)\\\text{Line 3: }21+11(2)\\\text{Line 4: }21+22\\\text{Line 5: }43[/tex]
The mistake is in Line 3. Danny cannot just combine 5+6(2) into 11(2). Instead, he should multiply 6(2) and then add. Thus, the correct solution is:
[tex]\text{Line 1: } 21+35\div7+6(2)\\\text{Line 2: }21+5+6(2)\\\text{Line 3: }21+5+12\\\text{Line 4: }26+12\\\text{Line 5: }38[/tex]
The cost of an electrical gadget and the cost of a plumbing material were in the ratio 8:6 last year, this year each cost was reduced by GHÇ 4.00 and their ratio changed to 7:5 respectively. Taking the Initial cost of the electrical gadget to be GHÇp Calculate the value of p and q
Answer
p/q = 8/6
Make p the subject
p = 8q/6........equation 1
This year the price was reduced by 4
p-4/q-4 = 7/5
Cross multiple
5(p-4) = 7(q-4)
5p-20 = 7q-28
5p - 7q = -8 .......equation 2
Sub 8q/6 for p in equation 1
5(8q/6) - 7q = -8
Multiply through by 6
40q-42q=-48
-2q=-48
q=24
Sub 24 for q in equation 1
p= 8(24)/6
p= 192/6
p= 32.....
Check the answer for confirmation.
Thanks.
MAAM or SIR I AM FACING PROBLEM TO SOLVE THESE QUESTION WOULD YOU HELP ME WITH IT
Answer:
1. Kate travelled more by 83.87km 2. = 42.5, 85 3. a= 2570 b= 348.9 c= 0.0048 d= 0.765 4. = 15.25
Step-by-step explanation:
1. 320.25km- 236.38km = 83.87km.
2. 8.5x5= 42.5, 8.5x10 = 85.
3. a= 2570 b= 348.9 c= 0.0048 d= 0.765
4. 17.75- 2.5 = 15.25.
hope you found this helpful :)
Which constants could each equation be multiplied by to eliminate the x-variable using addition in this system of equations? 2 x + 3 y = 25. Negative 3 x + 4 y = 22. The first equation can be multiplied by –3 and the second equation by 2. The first equation can be multiplied by –4 and the second equation by 2. The first equation can be multiplied by 3 and the second equation by 2. The first equation can be multiplied by 4 and the second equation by –3.
Answer:
The first equation can be multiplied by 3 and the second equation by 2.
Step-by-step explanation:
We are given the following system of equations:
[tex]\boxed{\left \{ {{2x+3y=25} \atop {-3x+4y=22}} \right.}[/tex]
To eliminate a variable in the equation, they must cancel out. For instance, if x = 1, in order to cancel out the numbers, you must add -1.
To multiply an equation, you must apply the constant that you are multiplying by to all constants and coefficients of the equation. For example, to multiply 2x + 4y = 8 by 3, you must multiply 2x by 3, 4y by 3, and 8 by 3.
Therefore, using this information, you can attempt each answer set and test the possibilities.
Answer Choice A
If you multiply the first equation by -3, you will get -6x - 9y = -75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -6 + -6 gives you -12, so these do not cancel out.
Answer Choice B
If you multiply the first equation by -4, you will get -8x - 12y = -100. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -8 + -6 gives you -14, so these do not cancel out.
Answer Choice C
If you multiply the first equation by 3, you will get 6x + 9y = 75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding 6 + -6 gives you 0, so these do cancel out.
Answer Choice D
If you multiply the first equation by 4, you will get 8x + 12y = 100. If you multiply the second equation by -3, you will get 9x - 12y = -66. Adding 8 + -9 gives you -1, so these do not cancel out.
A race car is traveling at a constant speed of 150 miles per hour. How many feet does it travel in 5seconds
Answer:
1100 ft
Step-by-step explanation:
1 mile per hour is equivalent to 22 ft in 15 seconds, so we can convert the speed to distance using ...
distance = speed × time
distance = (150 mi/h) (22/15 ft/s)/(1 mi/h) (5 s) = (150·22·5)/15 ft = 1100 ft
The car travels 1100 feet in 5 seconds.
Ingredients for 16 brownies:
2/3 cup butter, 5 ounces unsweetened chocolate, 1 and 1/2 cups sugar, 2 teaspoons vanilla, 2 eggs, 1 cup
How much of each ingredient is needed to make 12 brownies?
Answer:
1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.
Step-by-step explanation:
There are several ways to solve this, I like using proportions.
(You could also find 3/4 of every ingredient since 12 is 3/4s of 16)
We can do this by temporarily naming the amount of each ingredient a variable, and then using the proportion to find the variable.
Note that in a given proportion such as:
a/b=c/d
will always equal
a*d=b*c
This is known as cross multiplying.
For each ingredient I'm going to set up the following proportion:
[tex]\frac{amount of given ingredient in 16 brownies}{16 (number of brownies)} = \frac{variable (amount of given ingredient in 12 brownies}{12 (new number of brownies)}[/tex]
Now we can start setting up proportions for every ingredient.
Butter:
(2/3)/16=b/12
(2/3)(12)=16b
8=16b
b=1/2
Chocolate:
5/16=c/12
60=16c
c=60/16
c=15/4
Sugar:
(3/2)/16=s/12
(3/2)(12)=16s
18=16s
s=18/16
s=9/8
Vanilla:
2/16=v/12
24=16v
v=24/16
v=3/2
Eggs:
2/16=e/12
24=16e
e=3/2
Flour:
1/16=f/12
12=16f
f=3/4
Therefore, the ingredients for 12 brownies would be:
1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.
Which measurement is closet to the total surface area of the triangular prism in square centimeters?
Answer:
Step-by-step explanation:
mxcm w dhvhhhvhhjjjbvgvhn jnjjhvghcghyjbvcchgvukchgcgvmbmhc
For the statement? below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim.
The standard deviation of the base price of a certain type of? all-terrain vehicle is at least ?$327.
Write the claim as a mathematical statement.
A. equals327
B. sigmagreater than327
C. sigmaless than or equals327
D. sigmanot equals327
E. sigmagreater than or equals327
F. sigmaless than327
Answer:
Option E - sigma greater than or equal to $327
Step-by-step explanation:
In this question, we are testing whether the standard deviation of the base price of a certain type of all-terrain vehicle is at least $327.
Now, standard deviation is denoted by the symbol sigma(σ). Since the test is saying it should be at least $327, it means it should either be equal to $327 or greater than $327.
Thus, we would use the symbol ≥ which means "greater than or equal to".
Thus, the claim as a mathematical statement would be;
sigma greater than or equal to $327
Identify the slope and line intercept for y = 3x + 1
Answer:
Intercept - 1
Slope - 3
Step-by-step explanation:
in y=mx+b
m is the slope and b is the y intercept
MARK AS BRAINLIEST An artist has a block of clay in the shape of a cube. The edges of the cube measure 3 inches. The artist will use the clay to make models of
pine trees. Each tree will be a solid cone with a base diameter of 1.5 inches and a height of 2 inches.
Part A
Determine the greatest number of clay pine trees that the artist can make. Show your work.
Answer:
22
Step-by-step explanation:
The volume of a cube is given as:
Cube volume = length × length × length
Since the edges of the cube measure 3 inches, this means that the length of the cube is 3 inches, therefore:
Cube volume = 3 inches × 3 inches × 3 inches = 27 in³
The pine tree is the shape of a cone with diameter of 1.5 inches and a height (h) of 2 inches. The radius (r) = diameter / 2 = 1.5 inches / 2 = 0.75 inches.
The volume of the cone = πr²(h/3) = π × (0.75)² × (2/3) = 1.178 in³
The number of pine trees that can be made = Volume of cube / Volume of cone = 27 / 1.178 = 22.9
The number of pine trees = 22
25. Michelle walks into class and yells out that she just got a new Gucci bag for 50% off. If she paid $120 for
the bag, how much was the original price without the discount?
Answer:
$240
Step-by-step explanation:
50% = 0.5
$120 ÷ 0.5 = $240
The original price without the discount is $240.
Hope that helps.