Answer:
6/6 or 1/1
Step-by-step explanation:
A standard number cube has 6 sides to it. Therefore there are 6 possibilities, as you can roll either a 1, 2, 3, 4, 5, or 6.
The question is asking what the probability is for not rolling a number more than 62. To reword the question to get rid of the confusing 'not', "What is the probability of rolling a number less than 62?"
All the possibilities on the dice are less than 62, therefore it is guaranteed you will not roll a number more than 62. The probability is 1, or written as a fraction 1/1, or 6/6, since 6 sides of the 6 sided cube are less than 62.
A company makes concrete paving stones in different sizes. Each stone has a volume of 30 cubic inches and a height of 3 inches. The stones have different lengths and width. No stone have a length or width of 1 or 2 inches. How many different paving stones, each with a different-size base, have a volume os 360 cubic inches?
There are 6 different paving stones with a different-size base that have a volume of 360 cubic inches.
To find the different paving stones with a volume of 360 cubic inches, we need to consider the possible combinations of length and width for each stone.
Given that each stone has a volume of 30 cubic inches and a height of 3 inches, we can calculate the area of the base by dividing the volume by the height. So, the area of the base is [tex]\( \frac{360}{3} = 120 \)[/tex] square inches.
Since no stone can have a length or width of 1 or 2 inches, we need to find all the possible combinations of length and width that result in an area of 120 square inches, excluding 1 and 2 inches.
One approach to finding these combinations is to factorize 120:
[tex]\[ 120 = 2 \times 2 \times 2 \times 3 \times 5 \][/tex]
Then, we can use these factors to form different pairs of length and width. However, we must remember that the length and width cannot be 1 or 2 inches. So, the possible lengths and widths could be:
[tex]\[ \text{Length} \times \text{Width} \]\[ 3 \times 40 \]\[ 4 \times 30 \]\[ 5 \times 24 \]\[ 6 \times 20 \]\[ 8 \times 15 \]\[ 10 \times 12 \][/tex]
These are all the combinations that result in a base area of 120 square inches. So, there are 6 different paving stones with a different-size base that have a volume of 360 cubic inches.
The Nelson family drank of a gallon of orange juice on Saturday morning and of a gallon of orange juice on Sunday morning. How much orange juice did they drink in All
Answer:
2 gallons of orange juice
Step-by-step explanation:
Final answer:
The Nelson family drank a total of 11/12 of a gallon of orange juice.
Explanation:
To find the total amount of orange juice the Nelson family drank, we need to add the amount they drank on Saturday morning and Sunday morning. They drank 1/4 of a gallon on Saturday and 2/3 of a gallon on Sunday. To add these fractions, we need to find a common denominator. The least common denominator (LCD) for 4 and 3 is 12.
Converting 1/4 to twelfth, we get 3/12. Converting 2/3 to twelfths, we get 8/12. Now we can add 3/12 + 8/12 to get a total of 11/12. Therefore, the Nelson family drank 11/12 of a gallon in total.
Which is equivalent to -9y+ 2x? (Choose all correct answers.) *
2x-9y
11x + 3y - 12y - 9x
-117
-11(y + x)
0
100 points! :) ASAP PLEASE!!!
Examine the steps used to solve the equation.
-3y + 2/3 = 2y - 4
1. 2/3 = 5y - 4
2. 14/3 = 5y
3. (1/5) 14/3 = (1/5) 5y
Evaluate the steps used to solve the equation, and then describe each step.
Step 1. (add 3y to both sides, subtract 3y form both sides, add 2y to both sides, subtract 2y to both sides)
Step 2. (add 4 to both sides, subtract 4 from both sides, multiply both sides by 4, divide both sides by 4)
Step 3. (add 5 to both sides, add 1/5 to both sides, subtract 5 from both sides, multiply both sides by 1/5)
What is the solution to the equation? y = (14/5 , 14/15 , 7/8 , 70/3)
Answer:
step1:add 3y to both sides
step2:add 4 to both sides
step3:multiply both sides by(1/5)
14/15
Step-by-step explanation:
The steps to solve the equation -3y + 2/3 = 2y - 4 are accurate and lead to the conclusion of y = 14/15.
Explanation:In examining the steps for solving the equation
-3y + 2/3 = 2y - 4
, we can conclude they are correctly performed.
Step 1: On the left side of the equation, add 3y and subtract 3y from the right side to consolidate y on one side of the equation, giving us 2/3 = 5y - 4. Step 2: On the right side of the equation, add 4 to both sides to isolate y further resulting in 14/3 = 5y. Step 3: Last step is to multiply both sides by 1/5 to solve for y thus getting y = 14/15.In summary, the steps are correctly structured and the solution to the equation is y = 14/15.
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How do you solve -5x - 5y = 0 and y = 8x
We solve the system of equations -5x - 5y = 0 and y = 8x using the substitution method. Substituting y = 8x into the first equation, then solving for x and y, we find that x = 0, y = 0.
Explanation:To solve the system of equations -5x - 5y = 0 and y = 8x we will use substitution method. The substitution method involves substituting the expression from one equation into the other equation. Here, we are given that y is equal to 8x, so we can substitute 8x in place of y in the first equation. That gives us:
-5x - 5*(8x) = 0
Solve this equation, we get x = 0. Now, substitute x = 0 in the second equation to find y. That gives us:
y = 8*0
So, y = 0. Therefore, the solution to the system of equations is x = 0, y = 0.
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please help with this asap ty
Answer:
9 : 7
Step-by-step explanation:
Given
4.5 : 3 [tex]\frac{1}{2}[/tex]
Multiply both parts of the ratio by 2 to clear the fractions, that is
= 9 : 7 ← in simplest form
Which dimensions can create more than one triangle? three angles measuring 75 degrees, 45 degrees, and 60 degrees three sides measuring 7 m, 10 m, and 12 m three angles measuring 40 degrees, 50 degrees, and 60 degrees three sides measuring 3 cm, 4 cm, and 5 cm
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:right
Paulokeeps track of his favorite baseball player batting average and notices the average is 0.4727272... .If the player has 55 bats what is the number of hits
Answer:
Number of hits of Paulo favorite baseball player is 26.
Step-by-step explanation:
Given:
Average of favorite baseball player = 0.47272727
Number of bats = 55
We need to find the number of hits.
Solution:
Let the number of hits be 'x'.
Now we know that.
Batting average can be calculated by dividing Number of hits from number of bats.
framing in equation form we get;
[tex]\frac{x}{55}=0.47272727[/tex]
Multiplying both side by 55 we get;
[tex]\frac{x}{55}\times 55=0.47272727\times 55\\\\x=26[/tex]
Hence Number of hits of Paulo favorite baseball player is 26.
Using the formula Number of hits = Batting average * Number of bats, Paul's favorite baseball player had approximately 26 hits from 55 bats, given a batting average of 0.4727272.
Explanation:To calculate the number of hits of the baseball player, if we know their batting average, we can use the formula:
Number of hits = Batting average * Number of bats
In this case, the batting average is 0.4727272. The number of bats is 55. By substituting these values into the formula, we get:
Number of hits = 0.4727272 * 55 = 26
So, the baseball player had 26 hits. Please note that in practical situation, number of hits should be a whole number, so we might round the result to the closest whole number.
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Carter Motor Company claims that its new sedan, the Libra, will average better than 26 miles per gallon in the city. Use μ, the true average mileage of the Libra.
Answer:
The true average mileage of the Libra Using Null hypothesis is as ;
H0:μ≤26
(Ha):μ >26
Step-by-step explanation:
Given:
Libra, will average better than 26 miles per gallon in the city
To Find:
Average mileage of the Libra.
Solution:
This problem is related to the null hypothesis and alternate hypothesis.
i.e Null Hypothesis is the statement which is true and statement which contradictory is called alternate hypothesis.
“reject H0” if the sample information favors the alternative hypothesis.
“do not reject H0” / “decline to reject H0” if the sample information is insufficient to reject the null hypothesis
So given that condition is libra will have average better than 26
So it will include 26 and above values .
i.e. True condition is called as null hypothesis (H0)
so true average will be greater than 26
So H0:μ≤26
And the Alternate hypothesis will be the contradictory to true condition
(Ha):μ >26 .
It is believed that a stock price for a particular company will grow at a rate of $5 per week with a standard deviation of $1. An investor believes the stock won’t grow as quickly. The changes in stock price is recorded for ten weeks and are as follows: $4, $3, $2, $3, $1, $7, $2, $1, $1, $2. Perform a hypothesis test using a 5% level of significance. What is the p-value?
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = $5
For the alternative hypothesis,
µ < $5
number of samples taken = 10
Sample mean, x = (4 + 3 + 2 + 3 + 1 + 7 + 2 + 1 + 1 + 2)/10 = 2.6
To determine sample standard deviation, s
s = √(summation(x - mean)/n
n = 12
Summation(x - mean) = (4 - 2.6)^2 + (3 - 2.6)^2 + (2 - 2.6)^2 + (3 - 2.6)^2 + (1 - 2.6)^2 + (7 - 2.6)^2 + (2 - 2.6)^2 + (1 - 2.6)^2 + (1 - 2.6)^2 + (2 - 2.6)^2 = 30.4
s = √30.4/10 = 1.74
Since the number of samples is 10 and no population standard deviation is given, the distribution is a student's t.
Since n = 10,
Degrees of freedom, df = n - 1 = 10 - 1 = 9
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.6
µ = population mean = 5
s = samples standard deviation = 1.74
t = (2.6 - 5)/(1.74/√10) = - 4.36
We would determine the p value at alpha = 0.05. using the t test calculator. It becomes
p = 0.000912
In this scenario, a hypothesis test is conducted with the null hypothesis positing that the stock's price growth rate is $5 per week. The calculated p-value ends up being less than the significance level (0.05), leading to the rejection of the null hypothesis. Therefore, there is statistical evidence to support the investor's belief that the stock's growth rate is less than $5 per week.
Explanation:We start by stating the null and alternative hypotheses. The null hypothesis (H0) is that the mean growth rate of the stock is $5 per week - as initially believed. The alternative hypothesis (Ha), which the investor believes, is that the mean growth rate is less than $5 per week.
To test these hypotheses, we first calculate the sample mean and standard deviation. The given observations for the ten weeks are: $4, $3, $2, $3, $1, $7, $2, $1, $1, $2. The mean of these values is $2.6. The standard deviation is approximately $1.72.
Next, we calculate the Z score, which is (sample mean - population mean) / (standard deviation / square root of the sample size). We therefore have (2.6 - 5) / (1.72 / √10) = -4.41.
Using a Z-score table or software, we then find the p-value associated with this Z-score. The result is a p-value significantly less than 0.05, which is our alpha (significance level). Therefore, we reject the null hypothesis. This implies that with a 5% significance level, there is enough statistical evidence suggesting that the stock's price growth rate is less than $5 per week.
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Answer quick for brainliest <3
Answer: proportional
Yes the table is proportional because for every 1 increase in x the increase in y is 5. Because the increase for every 1 x is 5 means it is proportional.
The diameter of a circle is 13 m find it’s circumference in terms of pi
The circumference of the circle is approximately 40.8406 m.
Explanation:The circumference of a circle can be found using the formula C = πd, where C is the circumference and d is the diameter of the circle.
In this case, the diameter of the circle is given as 13 m. So we can substitute this value into the formula to find the circumference:
C = 3.14159… x 13 m = 40.8406 m
Therefore, the circumference of the circle is approximately 40.8406 m.
Final answer:
The circumference of a circle with a diameter of 13 meters is expressed in terms of Pi as 13π meters.
Explanation:
The circumference of a circle is calculated using the formula C = πd, where C is the circumference, π (Pi) is a mathematical constant, and d is the diameter of the circle.
Given that the diameter is provided as 13 meters, we use this formula to find the circumference in terms of π.
Thus, the circumference C is equal to:
C = π × 13 m
Since we are expressing our answer in terms of π, there's no need to calculate the numeric value of π. However, if we need to use a value for practical purposes, π is approximately 3.14.
So for our purposes, the circumference in terms of π is simply 13π meters.
?/6 < 1/2 whats the missing number
Answer:
The missing number is either 1 or 2.
1/6 and 2/6 are both less than 1/2.
Theo recorded the gender and eye color of students walking in the hallway at his middle school. What is the experimental probability that the next student he sees will be a boy with brown eyes?
Final answer:
The experimental probability that the next student will be a boy with brown eyes cannot be determined without specific observational data. You would need the number of boys with brown eyes and the total number of students Theo observed to calculate it.
Explanation:
To find the experimental probability that the next student Theo sees will be a boy with brown eyes based on his observations, we need to count the number of boys with brown eyes that were observed and then divide by the total number of students observed. However, the data provided does not include specific information on the number of boys with brown eyes seen by Theo. To calculate the experimental probability, you would need that information, as it is defined by the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.
For example, if Theo observed 10 boys and 4 of them had brown eyes, and the total number of students observed was 30, then the experimental probability of the next student being a boy with brown eyes would be 4 out of 30, or 4/30. To express this as a percentage, divide 4 by 30 and then multiply by 100 to get 13.33%.
An object is translated from A (-6, -4) to A' (-18, -8). What is the translation rule?
Given:
An object is translated from A(-6, -4) to A'(-18,-8)
We need to determine the translation rule.
Translation rule:
The translation rule is given by
[tex]A(x,y)\rightarrow (x+h,y+k)\rightarrow A'(x,y)[/tex]
Substituting the coordinates of A and A', we get;
[tex]A(-6,-4)\rightarrow (-6+h,-4+k)\rightarrow A'(-18,-8)[/tex]
Equating the x and y coordinates, we get;
x - coordinate:
[tex]-6+h=-18[/tex]
[tex]h=-12[/tex]
Thus, the value of h is -12.
y - coordinate:
[tex]-4+k=-8[/tex]
[tex]k=-4[/tex]
Thus, the value of k is -4.
Hence, the translation rule is [tex](x,y)\rightarrow (x-12,y-4)[/tex]
Help me its so hard to understand
Ellie baked a round cookie cake for her sister birthday the radius of the cookie aas 6 inches . If ellies sister ate 1 /4 of the cookie cake about how many square inches did she eat
Answer:
28.3 square inches
Step-by-step explanation:
In the question, we are asked to calculate the portion of the area of the cake eaten by Ellie’s sister.
To calculate this, the first thing to do is to calculate the area of the cookie cake. Now, since it’s a round cake, then it must be circular in shape.
Hence we calculate the area.
mathematically the area of a circle can be calculated using the formula;
A = pi * r^2
here our r =6 inches
Substituting this, we have
A = 22/7 * 6 * 6 = approximately 113 sq. inches
we now move on to calculate the portion ate, which is a quarter
That would be 1/4 * 113 = 28.3 sq. inches was eaten
Answer:
28 Square inches
Step-by-step explanation:
Since the cookie is round, it is in a circular shape.
Radius of the Cookie Cake, r= 6 Inches
Area of a Circle [tex]=\pi r^2[/tex]
Therefore, the area of the whole cookie cake [tex]=\pi X 6^2 =113.097 \:Square\: Inches[/tex]
Since Ellie's Sister ate 1/4 of the cookie cake,
Area of cake eaten by Ellie's Sister
[tex]\frac{1}{4} X 113.097\\ =28.27[/tex]
Ellie's Sister ate approximately about 28 Square inches of cake.
What is the value of b?
Answer:
b = 10
Step-by-step explanation:
We know
x^2 / (24^2) - y^2/ ( b^2) = 1
equation: directrix x = a^2 / c = 576/26
a = 24
24^2/ c = 576/26
c = 26
so a^2 + b^2 = c^2
so 24^2 + b^2 = 26^2
b^2 = 26^2 - 24^2 = 100
b = 10
A right triangular prism is constructed so that its height is equal to the leg length of the base.
A right triangular prism is shown. The right triangles have 2 sides with a length of x. The length of the hypotenuse is unknown. The height of the prism is x.
What expression represents the volume of the prism, in cubic units?
a. One-halfx3
b. One-halfx2 + x
c. 2x3
d. 2x2+ x
Answer:
the answer is A
Step-by-step explanation:
The volume of the right triangular prism is x³/2 cubic units.
What is volume?Volume is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Given that in a right triangular prism its height is equal to the leg length of the base.
we need to find the expression for the volume,
The volume of a right triangular prism is:
V = The base area x the height
Therefore,
V = 1/2 · x · x · x
Hence the volume of the right triangular prism is x³/2 cubic units.
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Maddie’s salary is £16,000 and she is due to get an increase of 5%. How much will this increase be
Answer:
800
Step-by-step explanation:
16,000 x 0.05 = 800
The Fan Cost Index (FCI) represents the cost of four average-price tickets, refreshments, and souvenirs to a sporting event. The FCIs for an independent tennis league and an independent basketball league totaled $123.62. The basketball FCI was $ 6.98 more than that of tennis FCI.
What were the FCIs for these sports?
Answer:
The FCI for tennis league is $ 58.32 and FCI for basketball league is $65.30
Step-by-step explanation:
We have been given the following data:
The FCIs for an independent tennis league and an independent basketball league totaled $123.62
Let the FCI for tennis league be "x" and the FCI for basketball league be "y". Since, the total for both leagues is $ 123.62, this means the sum of x and y must be $ 123.62. Using this we can set up our first equation as:
x + y = 123.62 Equation 1
The basketball FCI was $ 6.98 more than that of tennis FCI. This means y would be more than x by 6.98. Using this we can set up our second equation as:
y = x + 6.98 Equation 2
Substituting the value of y from Equation 2 to Equation 1, gives us:
x + x + 6.98 = 123.62
2x + 6.98 = 123.62
2x = 123.62 - 6.98
2x = 116.64
x = 116.64/2
x = 58.32
Using the value of x in Equation 2 gives us:
y = x + 6.98 = 58.32 + 6.98 = 65.3
Therefore, the FCI for tennis league is $ 58.32 and FCI for basketball league is $65.30
Find the sum of -1676 +(-1669) + (-1662) + ... +(-115) +(-108).
Answer:
-200,700
Step-by-step explanation:
(-1676+-108)/2 = -892 x 225 = -200,700
225 = number of terms -108 + 1676 / 7
pls answer the question in the pic i will mark u as brainliest
Answer:
2 ft³
Step-by-step explanation:
The volume (V) of the triangular pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the perpendicular height )
A = [tex]\frac{1}{2}[/tex] × 2 × 2 = 2 ft² ← area of triangular base and h = 3, thus
V = [tex]\frac{1}{3}[/tex] × 2 × 3 = 2 ft³
A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded
that:
a. If the butler is telling the truth, then so is the cook.
b. The cook and the gardener cannot both be telling the truth.
c. The gardener and the handyman are not both lying.
d. If the handyman is telling the truth then the cook is lying.
Answer:
Step-by-step explanation:
Step 1:we should turn the “facts” into logical expressions.
Step 2:Assign variables
Our variables are: b (for butler), c (for cook), g (for gardener), h (for handyman)
Step 3 . Let the value of true indicate that the person is telling the truth. For example, b = T means the butler is telling the truth. Then we can translate the statements as follows:
Check attachment
Step 4
We know all of these must hold. So we really want to know when (b→c)∧¬(c∧g)∧¬(¬g∧¬h)∧(h → ¬c) is true.
Step 5
Behold, another truth table task! If you work out the truth table, you see that this statement is only true when:
Check attachment
Step 6
Therefore we can say the butler and cook are definitely lying, but we can not determine if the gardener or handyman are lying. However, there are four variables in this problem. Instead, we can do this with some straight reasoning. Notice that:
If the butler is telling the truth, then by (a) the cook is telling the truth.
If the cook is telling the truth, then by (b) the gardener is lying.
If the gardener is lying, then by (c) the handyman is telling the truth.
If the handyman is telling the truth, they by (d) the cook is lying.
This leads to a contradiction (the cook can not be both telling the truth and lying)! Therefore the butler and cook must be lying. What about the gardener and the handyman? We don’t have enough information to figure out if they are lying. Since the cook is lying, we can’t use (b) to come to any conclusions about the gardener. Even if we are able to conclude that the gardener is telling the truth, we can’t use (c) to come to any conclusions about the handyman.
how do i calculate the height?
Answer:
3
Step-by-step explanation:
YS = DI = 6
A = YS * AI = 24
height = A/b = 24 / 8 = 3
Factor completely: 3x^2 + 12x + 7
Answer:
6x+12
Step-by-step explanation:
What is the measure of angle D
Answer:
D=142
Step-by-step explanation:
Answer:
14 degrees?
Step-by-step explanation:
The fifth graders went to the Dallas zoo. 84 kids went. The teachers where free but payed 5$ the total bill was 530$ how much was the entrance fee for each child
Answer:
what was paid exactly per student as entrance fee is $6.25
Step-by-step explanation:
In this question, we are told that some kids went to an excursion with their teachers and paid a certain total bill. we now need to know the amount paid per child as the entrance fee to the zoo.
Firstly, we need to subtract the amount paid by the teachers so we know exactly how much was spent on the students entrance fee alone.
subtracting the $5 from the total we have $530 - $5 = $525
Now to know what was paid as entrance fee per student, we simply divide this by the total number of students. That will be 525/84 = $6.25
This means that what was paid exactly per student as entrance fee is $6.25
The entrance fee per child at the Dallas zoo can be found by subtracting the teachers' payment from the total bill and then dividing it by the number of kids. In this case, the entrance fee per child is $6.31.
Explanation:The entrance fee for each child can be calculated by subtracting the amount paid by the teachers from the total bill and then dividing it by the number of kids:
Total bill - Teachers' payment = Amount paid by the kids
530$ - (5$ x Number of teachers) = Amount paid by the kids
530$ - (5$ x 0) = Amount paid by the kids
530$ = Amount paid by the kids
To find the entrance fee for each child, divide the amount paid by the number of kids:
Entrance fee per child = Amount paid by the kids / Number of kids
Entrance fee per child = 530$ / 84 kids
Entrance fee per child = $6.31.
Find the coordinates of the vertices of the figure after a reflection of the given axis. Then graph the reflection image.
Given:
The coordinates of the triangle ABC are (3,3), (6,5) and (2,1)
We need to determine the vertices of the triangle A'B'C' after reflection across y - axis.
Reflection across y - axis:
The rule to translate the coordinates across y - axis is given by
[tex](x,y)\implies (-x,y)[/tex]
Let us substitute the coordinates.
The coordinates of the point A' are
[tex]A(3,3)\implies A'(-3,3)[/tex]
The coordinates of the point B' are
[tex]B(6,5)\implies (-6,5)[/tex]
The coordinates of the point C' are
[tex]C(2,1)\implies (-2,1)[/tex]
Therefore, the coordinates of the triangle A'B'C' are (-3,3), (-6,5) and (-2,1).
Hence, Option C is the correct answer.
The image of the transformation is the figure represented by graph (b)
How to determine the image of the transformation
from the question, we have the following parameters that can be used in our computation:
The triangle
Also, we have the reflection axis to be
The y-axis
This means that the pre-image and the image of the reflection will be equidistant from the x-axis
Using the above as a guide, we have the following:
The image is (b)
Ana escribe conjuntos de cinco enteros positivos consecutivos con la siguiente propiedad: La suma de tres de los números es tan grande como la suma de los otros dos. ¿Cuántos conjuntos con esta propiedad ha escrito Ana?
Seleccione una:
a. 1
b. 2
c. 0
d. 3
e. Mas de 3
Answer:
a) 1.
Step-by-step explanation:
Supongamos que el primer número entero positivo es a tal que a ∈ Z⁺.
Luego, el conjunto de los cinco enteros positivos se puede expresar como
A = {a; a+1; a+2; a+3; a+4}
Dada la condición del problema, se debe cumplir que
a + (a+1) + (a+2) = (a+3) + (a+4)
⇒ 3a + 3 = 2a + 7
Resolviendo la ecuación resulta
a = 4
Luego, el conjunto A nos resulta
A = {4; 5; 6; 7; 8}
Puede concluirse que sólo un conjunto cumple con esta condición.