The distance covered by the car with 12 gallons of gasoline is 200 miles.
Given,
Distance travelled by a car with full tank gasoline = 300 miles
The capacity of the car's tank = 18 gallons
We have to find the distance covered by the car with 12 gallons of gasoline;
Here,
x be the distance covered by the car with 12 gallons of gasoline
Then,
300/18 = x/12
x = (300 x 12) / 18
x = (300 x 2) / 3
x = 100 x 2
x = 200 miles
That is,
The car will cover 200 miles with 12 gallons of gasoline.
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Use the grid to help you fill in the blank.
0.9 × ___ = 0.27
Answer:
0.3
Step-by-step explanation:
0.9 times 0.3 equals 0.27
14.2: Prove Pythagoras Right 15 min
Elena is playing with the equivalent ratios she wrote in the warm-up. She rewrites
=as a² = xc. Diego notices and comments, "I got b2 = yc. The a² and remind me
of the Pythagorean Theorem." Elena says, "The Pythagorean Theorem says that
a² + b² = ².1 bet we could figure out how to show that."
a
h
1. How did Elena get from = to a² = xc?
2. What equivalent ratios of side lengths did Diego use to get b² = yc?
In the following passage we have proven the Pythagoras' theorem.
What is Pythagoras' theorem?
The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Here given in the question that one side of the wall 5 feet
So as it is a rectangular bedroom it can be split into 2 right-angled triangles.
So the hypotenuse of the triangle is 13 feet
Now using the Pythagoras theorem we can find out the length of the other wall
b²=h²-p²
AB² + BC² = AD × AC + CD × AC
AB² + BC² = AC (AD + CD)
Since, AD + CD = AC
Therefore, AC² = AB² + BC²
So we have p² + b² = h².
Hence, we prove the Pythagoras theorem using two triangle.
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a shipment of 15 televisions contains 6 regular and 9 deluxe models. the manufacturer failed to mark the model designation on the cartons. if 3 cartons are selected at random, what is the probability that exactly 2 of them are the deluxe model? (round your answer to three decimal places.)
The probability that exactly 2 of them are the deluxe model =0.474
given that
there is a shipment of 15 televisions contains 6 regular and 9 deluxe models
now 3 cartons are selected at random
C(15,3) =[tex]\frac{15!}{(15-3)!3!}[/tex]
C(15,3) = [tex]\frac{13*14*15}{3*2*1}[/tex]
C(15,3) = 455
2 out of 9 deluxe models be picked
C(9,2) = [tex]\frac{9!}{(9-2)!2!}[/tex]
C(9,2) = [tex]\frac{8*9}{2*1}[/tex]
C(9,2) = 36
Each of these can be matched with 1 of 6 regular models
36 × 6 = 216
the probability that exactly 2 of them are the deluxe model
= [tex]\frac{216}{455}[/tex]
=0.474
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How many times does the digit 9 appear in the list of all integers from 1 - 500?
9 cannot be in the first postion.
2nd position but not third
5*1*9=45
3rd position but not second
5*9*1=45
2nd and third position
5*1*1=5 2 each so that is 10
45+45+10=100
9 appears in all integers from 1 to 500, 95 times.
9 total from
1-9: 1 time
10-19: 1 time
20-29: 1 time
30-39: 1 time
40-49: 1 time
50-59: 1 time
60-69: 1 time
70-79: 1 time
80-89 : 1 time
among 90 and 99
Between 1991 and 1998, one will occur.
then in 1999, 2 9.
9 from 90 to 99 is 10, thus
9+10 = 19 is the total number of 9s from 1 to 99.
In 1 to 99, there are so 19 9s.
similarly
the following:
19 9's in 100 to 199
19 9's in 200 to 299
19 9's in 300 to 399
19 9's in 400 to 499
Total 9s will therefore be
19+19+19+19+19+19 = 95 times
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An equation in slop intercept form the y intercept -5 the slope -1/2
Answer:
y=-1/2x-5
Step-by-step explanation:
Write an equation of a line in slope intercept form with a slope of 3/2 that passes through point (4,7).
Answer:
y
=
−
3
2
x
+
13
Explanation:
First write it using point-slope form:
y
−
7
=
−
3
2
(
x
−
4
)
Now simplify to slope-intercept:
Add 7 to each side:
y
=
−
3
2
(
x
−
4
)
+
7
Distribute
−
3
2
to each term in the parentheses:
y
=
−
3
2
x
+
6
+
7
y
=
−
3
2
x
+
13
hope I helped you:)
evaluate the summation for the indicated value of the variable. 1(1!) 2(2!) 3(3!) 4(4!) m(m!); m
The sum of the indicated variable is 23.
What is variable?
A variable is an alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables are specially employed in the case of pure mathematics expression or pure mathematics.
MAIN body:
the correct expression is as follows :
1(1!) +2(2!) +3(3!)+ 4(4!) ........+ m(m!) where m = 3
for m= 3
the expression becomes:
=1(1!) +2(2!) +3(3!)
factorial means we need to multiply the number until it reaches 1.
= 1*1 + 2*2*1 + 3*3*2*1
= 1+ 4+ 18
= 23
Hence the sum of expression is 23.
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suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. random samples of batteries are taken for each brand and the following data are recorded: sample 1: n1
The test statistic of two brands of batteries is -2.177.
How to calculate test statistic?[tex]n_1[/tex] = size of sample 1 = 16
[tex]n_2[/tex] = size of sample 2 = 21
[tex]\bar{x_1}[/tex] = mean of sample 1 = 210
[tex]\bar{x_2}[/tex] = mean of sample 2 = 225
[tex]\sigma_{1}[/tex] = standard deviation of sample 1 = 20
[tex]\sigma_{2}[/tex] = standard deviation of sample 2 = 23
T test is test for statistical hypothesis that follows t-distribution table under null hypothesis. T test is used when test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. So, for this case we use t test for test statistic,
t = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}[/tex]
t = [tex]\frac{210-225}{\sqrt{\frac{20^2}{16}+\frac{23^2}{21}}}[/tex]
t = [tex]\frac{-15}{\sqrt{\frac{400}{16}+\frac{529}{21}}}[/tex]
t = -15 / 7.0845
t = -2.117
Thus, the two brands of batteries have test statistic result is -2.117
Your question is incomplete, but most probably your full question was
Suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. Random samples of batteries are taken for each brand and the following data are recorded:
Sample 1: n1= 16, X1 = 210, s1= 20
Sample 2: n2= 21, X2 = 225, s2= 23
What is the test statistic assuming unequal population standard deviations?
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if a cup of diced cucumbers weighs 5.3 ounces, how many pounds of prepped cucumbers will you need for your 140 house salads?
46 pounds of prepped cucumbers are needed for 140 house salads.
It is given that one cup of diced cucumbers weighs 5.3 ounces.
Also, we know that one pound= 16 ounces or 1-ounce measure 1/16 pounds, we can do it in any way.
Thus, firstly, we will convert the ounces into pounds.
thus, 5.3 ounces= 5.3/16 pounds
Now, we need prepped cucumbers for 140 house salads, According to the given question.
thus, pounds needed for 140 house salads= 5.3/16*140
=> 46 pounds (nearly)
Thus, 140 house salads need nearly 46 pounds of cucumbers.
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4. Identify each of the following polygons:
Answer:
Step-by-step explanation:
1. Square
2. Rhombus
3. Trapezoid
4. Diamond
5. Octogon
6. Triangle
7. Pentagon
8. Hexagon
9. Triangle?
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If y = 21 when x = 14, find y when x = 40 .
ur answer should have ,60
Answer:
see explanation
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 21 when x = 14 , then
21 = 14k ( divide both sides by 14 )
[tex]\frac{21}{14}[/tex] = k , that is
k = [tex]\frac{3}{2}[/tex] = 1.5
y = 1.5x ← equation of variation
when x = 40 , then
y = 1.5 × 40 = 60
ab³ (5a²-4ab+b²) multiply
Answer: The correct answer is 5a^3b^3 − 4a^2b^4 + ab^5
Step-by-step explanation:
ab^3 (5a^2 − 4ab + b^2)
Multiply together:
(ab^3)*(5a^2 + −4ab + b^2)
(ab^3)*(5a^2) + (ab^3)*(−4ab) + (ab^3)*(b^2)
= 5a^3b^3 − 4a^2b^4 + ab^5
Answer:
[tex]5a^3b^3-4a^2b^4+ab^5[/tex]
Step-by-step explanation:
Given expression:
[tex]ab^3(5a^2-4ab+b^2)[/tex]
Apply the distributive property a(b - c + d) = ab - ac + ad :
[tex]\implies ab^3 \cdot5 a^2-ab^3 \cdot 4ab+ab^3 \cdot b^2[/tex]
Collect like terms:
[tex]\implies 5aa^2b^3-4aabb^3+ab^2b^3[/tex]
Apply the exponent rule a = a¹ :
[tex]\implies 5a^1a^2b^3-4a^1a^1b^1b^3+a^1b^2b^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 5a^{(1+2)}b^3-4a^{(1+1)}b^{(1+3)}+a^1b^{(2+3)}[/tex]
Simplify:
[tex]\implies 5a^3b^3-4a^2b^4+ab^5[/tex]
A given triangle has vertices at (-3,1) (2,4) and (5,-3) . If the triangle were rotated 180 degrees counterclockwise, the new coordinates would be ?
The new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
Define transformations.A function, f, that maps to itself are known as a transformation, or f: X → X. The transformation results in the pre-image X becoming the picture X. This transformation can utilize any operation, or a combination of operations, including translation, rotation, reflection, and dilation.
Given, the triangle vertices (-3, 1) (2, 4), and (5, -3).
When the triangle turned 180 degrees counterclockwise, we must determine the new coordinates;
When we rotate 180 degree counterclockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
Therefore, the new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
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Question 1 of 10 Which statements describe the function f(x) = 2(x-4)4? A. It has 3 zeros and at most 4 relative maximums or minimums. B. It is a translation of the parent function 4 units to the left. C. It has 4 zeros and at most 3 relative maximums or minimums. D. Both ends of the graph of the function go up. E. The left end of the graph of the function goes up, and the right end goes down. F. It is a translation of the parent function 4 units to the right. SUBMiT
Answer:
C. It has 4 zeros and at most 3 relative maximums or minimums. D. Both ends of the graph of the function go up.F. It is a translation of the parent function 4 units to the right.Step-by-step explanation:
You want the statements that describe the function f(x) = 2(x -4)⁴.
DegreeThe degree of the function is the exponent: 4. This means the function has 4 zeros.
The maximum number of relative extrema is 1 less than the degree. The function has at most 3 relative maximums or minimums.
The even degree means both ends of the graph go in the same direction.
Leading coefficientThe leading coefficient of 2 is positive, so the ends of the function will go up.
Horizontal translationIn the parent function f(x) = x⁴, the value of x has been replaced by (x-4). This causes the graph to be translated 4 units to the right.
__
Additional comment
This function has a zero at (4, 0) with multiplicity 4. There is a flat spot where the graph touches, but does not cross, the x-axis. As a consequence, there is only one minimum and no relative maximums.
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If line segment AB represents 50%, what is the length of a line segment that is 100%?
Answer:
it would be CD or 50%
Step-by-step explanation:
What number for C would make the equation below a perfect square trinomial.
x^2 +22x+c
(A)121
(B)72
(C)81
(D)96
The expression x^2 + 22x + c becomes a perfect square trinomial if the value of c is 121, so the correct option is A.
What value of C makes the expression a perfect square trinomial?A perfect square trinomial is written as:
(a + b)^2 = a^2 + 2ab + b^2
Here we have the expression:
x^2 + 22x + c
We can rewrite the second term in such a way that we get:
x^2 + 2*11*x + c
comparing this with the form of the general perfect square trinomial we can see that:
a = x
b = 11
Then the value of c must be 11^2 = 121
Then we have:
x^2 + 2*11*x + 121 = (x + 11)^2
The correct option is A.
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A baker makes a cake that requires 44 ounces of ingredients. The ratio of flour to sugar is 6:5. She didn’t like how the cake tasted so for the new cake, she changed the flour to sugar ratio to 7:6. If the amount of ounces she used increased to 91, how many more ounces of sugar did she add to the new cake? ( BE FAST PLEASE)
The amount of ounces of sugar she added to the new cake is 22 ounces
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the total ounces of ingredients in the cake be = 44 ounces
The ratio of flour to sugar is = 6 : 5
So , the amount of flour in 44 ounces = 6x
The amount of sugar in 44 ounces = 5x
And , the equation is
6x + 5x = 44
On simplifying the equation , we get
11x = 44
Divide by 11 on both sides , we get
x = 4
So , the total amount of sugar in 44 ounces of ingredients = 5x
Substitute the value for x = 4 , we get
Total amount of sugar in 44 ounces of ingredients = 20 ounces
And ,
Let the total ounces of ingredients in the new cake be = 91 ounces
The ratio of flour to sugar is = 7 : 6
So , the amount of flour in 91 ounces = 7y
The amount of sugar in 91 ounces = 6y
And , the equation is
7y + 6y = 91
On simplifying the equation , we get
13y = 91
Divide by 13 on both sides , we get
y = 7
So , the total amount of sugar in 91 ounces of ingredients = 6y
Substitute the value for y = 7 , we get
Total amount of sugar in 91 ounces of ingredients = 42 ounces
Therefore , the extra ounces of sugar the baker added to the new cake is =
Total amount of sugar in 91 ounces of ingredients - Total amount of sugar in 44 ounces of ingredients
The extra ounces of sugar the baker added to the new cake is = 42 - 20
Extra ounces of sugar the baker added to the new cake is = 22 ounces
Hence ,
The amount of ounces of sugar she added to the new cake is 22 ounces
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in a regression analysis, a(n) is used to predict a(n) . a. ordinal variable, ratio variable b. independent variable, dependent variable c. nominal variable, independent variable d. response variable, explanatory variable
In a regression analysis, a(n) is used to predict a(n) is known as option (b).independent variable, dependent variable.
Regression analysis:
In the concept of statistics, the regression analysis is useful to come up with a predictive model consisting of dependent and independent variables. And the R-squared value for a regression equation indicates the percentage of variability in the dependent variable being expressed by the variability in the independent variables.
Given,
Here we need to find the type of variable for a regression analysis, a(n) is used to predict a(n).
As per the definition of regression analysis, in the given question, we have two variable there are
=> a(n)
After prediction, the predicted value of a(n).
Here the first one is the independent variable because the this value is the based to predict the value of the other one is the dependent variable.
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if you are using 5.25% (mass/mass) bleach solution and you determine that the density of the bleach solution is 1.08 g/ml, how many moles of sodium hypochlorite are present in a 4.00 ml sample?
0.00305 moles of sodium hypochlorite are present in a 4.00 ml sample.
A mole is the mass of a substance made up of the same number of fundamental components. Atoms in a 12-gram example are identical to 12C. Depending on the substance, the fundamental units may be molecules, atoms, or formula units.
A mole fraction shows how many chemical elements are present. The value of 6.023 x 1023 is equal to one mole of any substance (Avagadro number). It can be used to quantify the chemical reaction's byproducts. The symbol for the unit is mol.
The number of moles formula is denoted by the following expression.
The mass of material / Mass of one mole equals the number of moles.
moles of NaClO = mass of sample×density of bleach solution×mass of bleach solution×1 mol/ mass of NaClO
= 4.00×1.08×0.0525/74.4 g of NaClO
= 0.00305.
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Can someone help me with this
Answer:
Step-by-step explanation:
What are you supposed to do?
the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km. what is the difference between these distances?
HELPPPPPPPPPPPP ASAP!!!!
The difference between these distances on the Earth is 3.32 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.
The difference will be:
= 4.00x10^4 km - 6.8x10^3 km.
= 3.32 × 10⁴
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f(x) = 2x²+ 3x - 14.
Answer:
Step-by-step explanation:
domain = all real numbers
range = {-121/8,∞)x-intercepts (2,0)
y-intercepts (0,-14)
vertex = minimum (-3/1 - 121/8)
Answer: Okay so I got,
1) x intercept = (2, 0), (-7/2, 0) and y intercept (0, -14)
2) 'x' equals to..
-Exact Form: 2, -7/2
-Decimal Form: 2, -3.5
Hope this helps!
josh was preparing a speech about home real estate and wanted to give an idea how home prices had fallen in all seven recognized neighborhoods in his city. he found that the rounded percentage decreases were 3, 3, 5, 6, 7, 7, and 19. why would using the mean, or average, decrease be misleading?
The mean of the decrease in rounded percentage of home is 7.14 which would used as misleading the about data as raw data very far away from 7.14.
As given in the question,
Given rounded percentage decrease in home price is:
3, 3, 5, 6, 7, 7, 19
Mean of the rounded percentage
= ( Sum of all the values)/ (Number of values)
= ( 3 + 3 + 5 + 6 + 7 + 7 + 19) / 7
= 50 /7
=7.1428
= 7.14
7.14 is very far away from 3 and 19.
Mean is not representing the correct information of the home price.
Using mean is misleading the correct information about percentage decrease.
Therefore, value of the mean is equal to 7.14 which mislead the decrease percentage.
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each of two pesticide brands is applied to 100 containers of fire ants. brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours.
The pValue is 0.15625 > 0.05 when brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.
Let A represent the new pesticide and B be the Ant Killer. Then, you are given that
Brand1 kills ants in 65 of 100 containers:
Xa = 65/100 = 0.65
Brand2 kills ants in 58 of 100 containers:
Xb = 58/100 = 0.58
You know need to find sample variance for both,
s²A =∑(Xi - Xa)
= 65(1-0.65)² + 35(0 - 0.65)²
= 22.7
s²B =∑(Xi - Xb)²
= 59(1-0.59)² + 41(0 - 0.59)²
= 24.19
You can know do a test for significance
t = (Xa - Xb) / √(sA /nA) +(sB/nB)
and derive the conclusion from there
Here, Null and alternative hypothesis are generally,
Alternative hypothesis
Here, there are three samples are assumed. They are:
i) Samples are taken independently
ii) Samples must be selected randomly
iii) n₁p₁ ≥ 5 , n₁q₁ ≥ 5, n₂p₂ ≥ 5, n₂q₂ ≥ 5
i.e., p₁ = 0.65 ; p₂ = 0.58 , n₁= 100
q₁ = 0.35 ; q₂ = 0.42 , n₂=100
Corresponding p-value at Z = 1.01722
p-value = 0.15625 > 0.05
Hence, the pValue is 0.15625 > 0.05 when brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.
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if you can notice the difference between 10- and 11-pound weights, which of the following weights could you differentiate from a 100-pound weight?
If we can notice the difference between 10- and 11-pound weight, we can differentiate 110-pound weight from a 100-pound weight.
What is weight?All things close to Earth are constantly subject to the force known as weight. All items are pulled downward toward the Earth's core by the gravity of the planet. On the other hand, weight is a measurement of how much gravity pulls an item downward. The mass of the thing has an impact on this force; the heavier the object, the stronger gravity's pull is. The force of gravity acting on a body is the most typical definition of weight given in introductory physics textbooks. This is sometimes formulated as W = mg, where W is the weight, m is the object's mass, and g is the acceleration due to gravity.
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Colorful wool is being woven into a scarf in cold, damp Ireland. Wool is used for scarves, sweaters, hats, and gloves because it is a good insulator. If wool is a good insulator, what substance would be a good conductor?
A plastic
B fur
C cotton
D metal
Anyone know this? Kind of struggling.
Answer:
It's -5 + 3 basicaly because 2 negatives is one positive. So the answer is -2.
if the original recipe calls for 50 portions, 6oz each and the new recipe calls for 100 portions at 5oz each, what is the recipe conversion factor?
By using multiplication and division of integers, it can be calculated that
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
What is multiplication and division of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem where multiplication and division of integers is required
The original recipe calls for 50 portions, 6oz each
Required yield of the original recipe = 50 [tex]\times[/tex] 6 = 300 oz
The new recipe calls for 100 portions at 5oz each
Required yield of the new recipe = 100 [tex]\times[/tex] 5 = 500 oz
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
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If (x-2)(x-4)= (x - h)² + k, then what is the value of k?
If the nth term of a number sequence is n^2 + 2n,
find the first 3 terms and the 10th term.
Answer:
3, 8, 15 and 120
Step-by-step explanation:
to find the first 3 terms, substitute n = 1, 2, 3 into the nth term rule
n = 1 : 1² + 2(1) = 1 + 2 = 3
n = 2 : 2² + 2(2) = 4 + 4 = 8
n = 3 : 3² + 2(3) = 9 + 6 = 15
the first 3 terms are 3, 8, 15
to find the 10th term , substitute n = 10 into the rule
n = 10 : 10² + 2(10) = 100 + 20 = 120