To find [tex]\frac{2}{3}[/tex] of a whole number, you can divide the number by 3 and then multiply the result by 2.
For example, if you want to find [tex]\frac{2}{3}[/tex] of the number 15, you can perform the following calculation:
[tex]\frac{2}{3}[/tex] × 15 = 10
This means that [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.
You can also find [tex]\frac{2}{3}[/tex] of a whole number by dividing the number by 3 and then multiplying the result by 2.
For example:
[tex]\frac{15}{3}[/tex] = 5
2 × 5 = 10
So, [tex]\frac{2}{3}[/tex] of the number 15 is also equal to 10.
Alternatively, you can find [tex]\frac{2}{3}[/tex] of a number by expressing it as a decimal. [tex]\frac{2}{3}[/tex] can be expressed as 0.6666666667, so you can multiply the whole number by 0.6666666667 to find [tex]\frac{2}{3}[/tex] of it. For example:
0.6666666667 × 15 = 10
So [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.
A whole number is a positive integer that is greater than 0, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc. Whole numbers do not include fractions, decimals, or negatives.
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How do you divide 56.87 by 14 with explanation?
! for all values of x, x² + 2x +4 = (x + 2)² + a( x + 2) + b where a and b are constants. what is the value of a ?
The value of a in the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b is equal to -2.
How to solve the constant "a" in the quadratic equation.We shall first expand the right hand side and express it in form of the left hand side of the quadratic equation, and then compare their coefficients to derive the value of the constant as follows;
Left hand side; {open brackets}
(x + 2)² + a( x + 2) + b = x² + 4x + 4 + ax + 2a + b
(x + 2)² + a( x + 2) + b = x² + 4x + ax + 4 + b {group like terms}
(x + 2)² + a( x + 2) + b = x² + (4 + a)x + 4 + b
such that :
x² + 2x +4 = (x + 2)² + a( x + 2) + b, then;
x² + 2x +4 = x² + (4 + a)x + 4 + b
by comparing coefficients, we have that;
4 + a = 2
a = 2 - 4 {subtract 4 from both sides}
a = -2
Therefore, for all values of x, the constant a = -2 for the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b.
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this data is normally distributed. what percent of the data is in the shaded region 68% 50% 95% 99.7%
As per the empirical rule, the percent of data in the shaded region is 68%.
In statistics, the empirical rule states that When you use a standard normal distribution also known as Gaussian Distribution we have to consider the following
=> Around 68% of values fall within one standard deviation of the mean.
=> Around 95% of the values fall within two standard deviations from the mean.
=> Other all of the values are about 99.7% that fall within three standard deviations from the mean.
Therefore, this facts are the 68 95 99.7 rule. And it is also called the Empirical Rule because the rule originally came from observations.
Here we have given the the data is normally distributed. And we need to find the percent of data is in the shaded region.
While we looking into the following diagram and according to empirical rule,68% of the data falls within one standard deviation of the mean.
Because, the center part is the shaded region,
So, it can be calculated as,
=> 34 + 34 = 68%
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please help me do this I've been stuck for over an hour
Find the missing length indicated. Leave your answer in simplest radical form.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
so the longest leg of the larger triangle will be "z" and the shorter leg of it will be "y", so let's find those fellows using proportions
[tex]\cfrac{x}{16}=\cfrac{9}{x}\implies x^2=144\implies x=\sqrt{144}\implies \boxed{x=12} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{x}=\cfrac{25}{16}\implies \cfrac{y}{12}=\cfrac{25}{16}\implies y=\cfrac{(12)(25)}{16}\implies \boxed{y=\cfrac{75}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{z}=\cfrac{9}{x}\implies \cfrac{~~ \frac{75 }{4 } ~~}{z}=\cfrac{9}{12}\implies \cfrac{75}{4z}=\cfrac{3}{4}\implies 300=12z \\\\\\ \cfrac{300}{12}=z\implies \boxed{25=z}[/tex]
if length of a rectangle is (x+7) and breath is (x+5). find the area of the rectangle
Step-by-step explanation:
Area of rectangle is length x breadth.
Area = (x + 7)(x + 5)
= (x² + 5x + 7x + 35)
= (x² + 12x + 35)
you toss a pair of six-sided dice. (a) determine the number of possible pairs of outcomes. (recall that there are six possible outcomes for each die.)
36 is the number of possible pairs of outcomes by probability.
What is a probability answer?
Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.
The probability value is given as a number between 0 and 1. Probabilities are always between 0 and 1. The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes.
We have two dice in this question. A die is known to be make up of 6 faces.
Therefore the number of faces for two dice = 6*6 = 36
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Write an explicit
formula for an, the nth term of the sequence 2, 4, 8, ..
Answer:
formula: Tn=a+(n-1)d
Step-by-step explanation:
Tn=2+(n-1)2
Explain what the symbol Z 0.05 represents and state its value: (choose one of the following answers..) a. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =1.65. b. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being less than that value is 0.05. The value is Z0.05 =1.65. c. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =2.58. d. Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being less than that value is 0.05. The value is Z0.05 =2.58.
Option 'a' is the correct answer.
Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =1.65.
In a normal distribution, data points are referred to as x, whereas in a z-distribution, they are referred to as z or z scores. A z score is a standard score that indicates how many standard deviations a given number (x) is from the mean:
If your x value is higher than the mean, your z score will be positive.If your z score is negative, it indicates that your x value is below the meanYour x value is the same as the mean if your z score is zero.Every z score has a corresponding p-value that indicates the likelihood that all values below or above that z score will occur.
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What is the half of 1.875 ? explain in detail ?
The half of the mentioned number after performing multiplication with 1/2 is 0.9375.
The half of 1.875 can be calculated by multiplying with (1/2). Half refers to two parts of one thing and hence it represented as the fraction 1/2. So, to find the half, we will multiply the mentioned number with 1/2.
Half value = 1.875 × 1/2
Now performing division and multiplication on Right Hand Side of the equation
Half value = 1.875/2
Half value = 0.9375
Thus, based on the division, the half of 1.875 is 0.9375.
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Solvex² - 5x 24 = 0 by factoring.
The solutions are x =
and x =
x = 8 , -3 are the factor of x .
What is factor ?
The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them.
Factors are the figures that can divide an amount precisely. There is therefore no residual after division.
x² - 5x - 24 = 0
x² - ( 8 - 3 )x - 24 = 0
x² - 8x + 3x - 24 = 0
x(x - 8 ) + 3 ( x - 8) = 0
( x + 3 ) ( x - 8 ) = 0
x = 8 , -3
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The complete question is -
x² - 5x - 24 = 0 by factoring.
The solutions are x =
homework due now!!!!!!!!!!!
Answer:
Option D: 7/3x
Step-by-step explanation:
Because this line passes through the origin (0,0), we know that there is know b-value according to the equation y = mx + b. To figure out the equation, we must first calculate the slope of the linear function.
Slope = △y/△x
△y (change in y) = -7
△x (change in x) = -3
Therefore, the slope is 7/3 and the equation is y = 7/3x.
I need help.... I can't figure it out!!
The area of the given irregular figure is 143 square inches.
What is area of irregular figure?
We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.
We have to divide the given irregular figure into known shapes.
That is rectangle and square.
Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.
So, the area of irregular figure is,
Area = Area of rectangle + Area of rectangle + Area of square
= (7 x 10) + (12 x 4) + 5^2
= 70 + 48 + 25
Area = 143
Hence, the area of the given irregular figure is 143 square inches.
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Which of the following is quadratic equation whose quadratic roots are 2 and 3?
The required quadratic equation which has the roots -2, and -3 is (C) x²+5x+6=0.
What is a quadratic equation?Any equation in algebra that can be written in the standard form where x stands for an unspecified amount, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
Factoring, using square roots, completing the square, and the quadratic formula is the four ways to solve a quadratic problem.
So, the product of a quadratic equation's elements can be used to represent any quadratic equation.
The necessary equation is created as follows:
(x - (-2))(x - (-3)) = 0
(x + 2)(x + 3) = 0
x² + 5x + 6 = 0
Therefore, the required quadratic equation which has the roots -2, and -3 is (C) x² + 5x + 6 = 0.
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Correct question:
Form a quadratic equation whose roots are -2,-3.
(A) x² - 6x + 5 = 0
(B) x² - 5x - 6 = 0
(C) x² + 5x + 6 = 0
(D) x² - 5x + 6 = 0
Write a triangle congruence statement
Edwin wants to know the height of a water tower. If the water tower casts a shadow 12 yards
long and a nearby street sign that is 3 yards tall casts a shadow 4 yards long, then how tall is the water tower?
one of the requirements of regression analysis is called the multicollinearity assumption. how is multicollinearity defined?
Multicollinearity can be defined as when two independent variables are correlated, multicollinearity occurs. Reason: Only the interactions between the independent variables are considered multicollinear.
Multicollinearity is the prevalence of excessive intercorrelations amongst or extra impartial variables in a more than one regression model. Multicollinearity: Multicollinearity exists whilst or extra of the explanatory variables are extraordinarily correlated.
This is a hassle as it could be tough to disentangle which ones first-rate explains any shared variance with the outcome. It additionally indicates that the 2 variables may also in reality constitute the identical underlying factor. Multicollinearity takes place whilst or extra impartial variables are extraordinarily correlated with each other in a regression model. This method that an impartial variable may be anticipated from any other impartial variable in a regression model.
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Let
ƒ(x) = (x + 2)² +3
g(x)=2x+6
How many boxes of markers should the teacher buy for a class of 30 students? Explain your answer.
Answer: 6 boxes of 5 markers in each box
Step-by-step explanation:
1. Consider the factors of 30
30: 1, 2, 3, 5, 6, 10, 15 and 30
2. pick any 2 that make 30
5*6=30
3. Therefore buying 6 boxes of 5 markers each should do the trick,
Hope this helps
Answer: 6 boxes of 5 markers in each box
Step-by-step explanation:
5) Consider the equation : y=7x+8
and the linear function represented by the table of values below. Select all of the statements that are correct.
The correct students about the function are;
B: The function represented by the table has a greater rate of change.
C: The function y = 7x + 8 has the greatest y-intercept.
How to Interpret the Function Table?We are looking at the equation;
y = 7x + 8
The general equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, the slope of the given equation is 7 while the y-intercept is 8.
From the table, the rate of change which is also is simply the slope from the formula;
m = (y₂ - y₁)/(x₂ - x₁)
m = (32 - 16)/(4 - 2)
m = 8
Looking at the given options, only options that are correct are Options B and C.
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-(4x+20) < −7(x + 15/7)
Answer: x < 5/3
Step-by-step explanation:
-(4x + 20) < −7(x + 15/7) ............................ Question
-4x - 20 < -7(x + 15/7) ................................ Distribute
-4x - 20 < -7x - 15 ...................................... Distribute
-4x - 20 + 20 < -7x - 15 + 20 ................... Add 20 to both sides
-4x < -7x + 5 ............................................... Simplify
-4x + 7x < -7x + 5 + 7x ............................. Add 7x to both sides
3x < 5 .......................................................... Simplify
3x / 3 < 5 / 3 .............................................. Divide both sides by the same factor
x < 5/3 ......................................................... Simplify
-5-4-3-
-3--
(0, 2)
--5+
64
(-3,-7)
2 3 4 5 x
Which linear inequality is represented by the graph?
Oy<3x + 2
Oy> 3x+2
Oy< = x+2
Oy>=x+2
Answer:
b
Step-by-step explanation:
The equation that represents the graph will be y > 3x + 2. Then the correct option is B.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
From the graph, the two points are (0, 2) and (-3, -7). The region above the line is considered, then the equation is written as,
(y - 2) > [(2 + 7) / (0 + 3)] (x - 0)
y - 2 > 3x
y > 3x + 2
The equation that represents the graph will be y > 3x + 2. Then the correct option is B.
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Can someone explain how to simplify radicals, cube roots, and rational radicals? Also how do I simplify a radical that has exponents?
An expression with a square root is referred to as a radical expression.
How to simplify radicals, cube roots, and rational radicals?Radical simplification:
Find the biggest square factor of the radicand while simplifying a radical.When a radical's radicand doesn't have a square number factor, it is said to be in its simplest form.Eg : [tex]\frac{x^{\sqrt{9} } }{x^{\sqrt{4} } } =x^{3-2} = x^{1} = x[/tex]Cube root simplification:
The process here is the polar opposite of cubing a phrase. When calculating a term's cube root, we look for the word that, when multiplied by itself three times, yields the term we are calculating the cube root of.Eg : [tex]\sqrt[3]{27} =\sqrt[3]{3^{3} } = [3^{3}]^{\frac{1}{3}} = 3[/tex]Rational radical simplification :
Find the greatest radicand factor that is a perfect power of the index. Utilizing that factor, rewrite the radicand as the product of two factors.Use the product rule to rewrite the radical as the union of two radicals.Reduce the perfect power to its simplest form. Eg :[tex]\frac{2}{\sqrt{5} -1} \\\\=\frac{2}{\sqrt{5} -1} *\frac{\sqrt{5}+1}{\sqrt{5}+1} \\\\=\frac{2(\sqrt{5} +1) }{4} \\\\=\frac{\sqrt{5} +1 }{2}[/tex]
Exponential radical simplification :
Exponents should be multiplied together when you're simplifying exponential expressions that have been increased to another exponent. Working out each exponent the difficult way will demonstrate that this is true for both positive and negative exponents.Eg :[tex](5^{2} )^{3} \\=(5^{2} ) (5^{2} )(5^{2} )\\=25 *25*25\\=15625[/tex]
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a pair of 6-sided dice is thrown. someone tells you that both the dice are showing an even number. with this information, what is the probability of the total (when you sum up the dice) being equal to 8?
As per the given dice, the probability of the total being equal to 8 is 1/9 or 11.11%.
Probability:
In statistics, probability refers the possibility of the particular event.
Given,
Here we need to find the probability of the total (when you sum up the dice) being equal to 8.
In order to calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8.
Hence both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6).
So, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.
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What is the square root of "0.9"?
The value of [tex]\sqrt{0.9}[/tex] is 0.94868329805. You can't get an accurate answer since the square root is an irrational quantity. But I suppose you could just make it simpler.
The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.
The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of three is nine. and the square root of 9, √9 = 3.
Since, 3*3*0.1
= 9*0.1
= 0.9
[tex]\sqrt{3*3*0.1} \\[/tex]
= 3([tex]\sqrt{0.1}[/tex])
[tex]\sqrt{0.9}[/tex] ≈ 0.94868329805
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Correct Question:
What is the value of [tex]\sqrt{0.9}[/tex]
An electrician needs to buy 7 1/2 feet of electrical wire. There are 1 1/2 feet of wire on each spool. How many spools of wire should the electrician buy?
Answer:
5
Step-by-step explanation:
[tex]\frac{7.5}{1.5}[/tex] = 5
Given lines l, m, and n are parallel and cut by two transversal lines, find the value of x. Round your answer to the nearest tenth if necessary.
when lines l, m, and n are intersected by two transversal lines and are parallel, the value of x = 12.5 is obtained.
what is transversal lines ?A transversal in geometry is a line that, at two different places, traverses two lines in the same plane. If two or more additional lines in the Euclidean plane are parallel, transversals can help determine this.
Parallel lines l, m, and n are present.
These parallel lines cross two transversal lines.
theorem of intercept
Intercept lengths between parallel lines are proportionate.
[tex]\frac{16}{x} = \frac{23}{18}[/tex]
x = (16 * 18) /23
x = 12.5
when lines l, m, and n are intersected by two transversal lines and are parallel, the value of x = 12.5 is obtained.
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Help me on this problem!
Answer:
B. Since [tex]\triangle ABC \cong \triangle DEF[/tex] by SSS and [tex]\triangle DEF \cong \triangle GHJ[/tex] by SAS, [tex]\triangle ABC \cong \triangle GHJ[/tex] by the Transitive Property of Congruence.
The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS
How to determine the congruent statement and the reason?From the question, we have the following parameters that can be used in our computation:
Triangles = ABC, DEF and GHJ
There are several theorems that make any two triangles to be congruent
One of these theorems is the SSS congruent theorem
The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent
From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark
AC and GJ
CB and JH
This implies that these sides are congruent sides
For the triangle to be congruent by SSS, the following angles must also be congruent
AB must be congruent to GH
Hence, the congruent statement on the congruency of the triangles is (d)
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using the points 0,2 and -3,4 write an equation in slope intercept form
Answer: y=—2/3x+2
Step-by-step explanation:
What is the equation of a line perpendicular to y= 2z - 6 that passes through (5, 4)
Use the formula y = m x + b
Answer:
Step-by-step explanation:
balls
A veterinarian surveys households in her area to find out how many pets they own. She estimates that households have 1.8 pets on average, with a margin of error of ±0.4 pets. There are 1,200 households in her area.
1. The minimum number (Lower Limit) of pets one can find in the area is 1,680 pets, given the margin of error.
2. The maximum number (Upper Limit) of pets in the area will be 2,640 pets, given the margin of error.
What is the margin of error?The margin of error shows the statistical difference between actual and projected results in a random survey sample.
In other words, the margin of error reveals the level of unpredictability in research outcomes.
The statistical difference can be explained with an upper limit (maximum) and lower limit (minimum) between which the statistical value lies, thereby offering some level of confidence.
Average (mean) number of pets in each household = 1.8 pets
The margin of error = ±0.4 pets
The total number of households in the area = 1,200
Upper limit (maximum) of pets in the area = 2,640 pets (1,200 x 1.8 +0.4)
Lower limit (minimum) of pets in the area = 1,680 pets (1,200 x 1.8 - 0.4)
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Question Completion:What are the minimum and maximum numbers of pets you expect to find in her area?
