Answer: The smallest two-digit prime number such that reversing the digits of the number produces a composite number is 19
Step-by-step explanation:
11, which is the smallest two-digit prime number, 11 remains the same number when the digits are reversed, and it is a prime number, of course.
The next two-digit prime number is 13. 13 becomes the prime number 31 when the digits are reversed.
17 is the following two-digit prime number. The result of flipping the digits of 17 is 71, a prime number.
19 is the following two-digit prime number. Reversing the digits of 19 results in 91, which is composite because 7*13= 91
Thus, 19 is the answer.
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which of the following statements is true of random assignment and random sampling?
A. Random assignment is the same as random sampling
B. Random assignment, if effective, allows us to make sure the only difference between the various treatment groups is what we are studying
C. Random assignment allows us to obtain a sample representative of the population
D. All of the above
Answer:
Random assignment is necessary for internal validity, whereas random assignment is necessary for external validity
Step-by-step explanation:
Find the volume of the sphere.
Either enter an exact answer in terms of π or use 3.14 for π.
The volume of the sphere whose radius is 3 as represented in the task content above is; 113.04 units³.
What is the Volume of the sphere?It follows from the task content that the volume of the sphere which is as represented in the task content is to be determined.
Recall from geometry of solid shapes (3 - dimensional shapes), the volume of a sphere is given by the formula;
V = (4/3) π r³
where r = radius = 3.
Therefore, Volume, V of the sphere is;
V = (4/3) × 3.14 × 3³
V = 113.04 units³.
On this note, the volume of the sphere as described is; 113.04 units³.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed is $10865, based on the given parameters
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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How does electron pair repulsion determine the molecular shape/molecule geometry?.
Yes, the electron pair repulsion determines the molecular shape, we can use VSEPR to find out how.
What is VSEPR theory?
The amount of valence electron pairs present in the outermost shell is used by the valence shell electron repulsion theory (VSEPR) to predict the structure of molecules.
The number of valence shell electron bond pairs between atoms in a molecule is used in the valence shell electron repulsion theory (VSEPR), a model for predicting 3D molecular form.
VSEPR theory predicts that BeF2 should be a linear molecule, with a 180o angle between the two Be-F bonds.
The VSEPR theory, therefore, predicts a trigonal planar geometry for the BF3 molecule, with an F-B-F bond angle of 120o.
we can predict that a tetrahedral molecule in which the H-C-H bond angle is 109o28'.
Hence we can predict the molecular shape, using VSEPR theory.
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What is the respective name for perpendicular bisectors of the sides?.
Answer: circumcenter
Step-by-step explanation:
If you meant the point of intersection of the perpendicular bisectors, this should be your answer.
In order to solve for the variable in the equation 1 minus (x 2) 2 x = 5 (2 x minus 5) minus x, mikel first applies the distributive property. which equation is a result of this step? 1 minus x 2 2 x = 10 x minus 5 minus x 1 minus x minus 2 2 x = 10 x minus 25 minus x 1 minus x minus 1 2 x = 10 x minus 25 minus x 1 minus x minus 1 2 x = 10 x minus 5 minus x
In order to solve for the variable in the equation
We want to apply the distributive property to the given expression.
1 - x - 2 + 2x = 10x - 25 - x is the result of this step.
Let's see how to solve this:
Remember that the distributive property says that:
A*(B + C) = A*B + A*C.
Here we have the expression:
1 - (x + 2) + 2x = 5*(2x - 5) - x
We can apply the distributive property to the first term in the right side, we will get:
1 - (x + 2) + 2x = 5*(2x - 5) - x
1 - (x + 2) + 2x = 5*2x - 5*5 - x
1 - (x + 2) + 2x = 10x - 25 - x
Now we can also apply the distribute property to the second term in the left side:
1 - (x + 2) + 2x = 10x - 25 - x
1 - x - 2 + 2x = 10x - 25 - x
Hence the answer is, 1 - x - 2 + 2x = 10x - 25 - x is the result of this step.
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In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat. What is the percent of times her hit the ball.
The percent of times that Emerson hit the ball, given the number of times that he struck out was 68 %
How to find the percent of times?First, find the total number of times that Emerson had at bat:
= Game 1 + Game 2 + Games 3
= 90 + 120 + 140
= 350 times
The number of times Emerson missed was:
= 30 + 40 + 42
= 112 times
The number of times the ball was hit is therefore:
= 350 - 112
= 238 times
The percent of time the ball was hit:
= 238 / 350
= 68 %
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What is the answer to 68 plus 899
Find the measure of x.
40
45°
X
x = [?]
X
Round to the nearest tenth.
Answer:
x ≈ 28.3
Step-by-step explanation:
using the cosine ratio in the right triangle
cos45°= [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )
40 × cos45° = x , then
x ≈ 28.3 ( to the nearest tenth )
a study investigated whether there are differences between the mean iq level of people who were raised by their biological parents and those who were raised by someone else.what is the null hypothesis in this case?
There is no difference between the mean IQ levels of people who were reared by their natural parents and those who were not.
Hypothesis.1) Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 7002) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment.Depending on the information received, it might be supported or might not be supported at all.learn more about hypothesis click here:
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Cliff borrows $10 from his brother. The next day, he borrows another $15 from his brother. What integer represents the balance that he owes his brother?
Answer: $25
Step-by-step explanation:
Add 10 and 15 to get 25
Complete this synthetic division table.
According to the given synthetic table, the quotient is 5x³ - 5x² + 3x + 2 and remainder is 1.
Synthetic table:
Basically, the shortcut for polynomial division when the divisor is of the form x – a. And only numeric coefficients of the dividend are used when dividing with synthetic division.
Given,
Here we have the synthetic table.
Now, we have to solve this one.
In order to find the quotient and remainder, we have to do the following steps:
Step-1 : Write down the first coefficient 5
Step-2 : Multiply our root -3 by our last result 5 to get -15 [ (-3) × 5=-15 ]
Step-3 : Add new result -15 to the next coefficient of the dividend 10, and write down the sum -5, [ 10 + (-15)=-5 ]
Step-4 : Multiply our root -3 by our last result -5 to get 15 [ (-3) × (-5)=15 ]
Step-5 : Add new result 15 to the next coefficient of the dividend -12, and write down the sum 3, [ (-12) + 15=3 ]
Step-6 : Multiply our root -3 by our last result 3 to get -9 [ (-3) × 3=-9 ]
Step-7 : Add new result -9 to the next coefficient of the dividend 11, and write down the sum 2, [ 11 + (-9)=2 ]
Step-8 : Multiply our root -3 by our last result 2 to get -6 [ (-3) × 2=-6 ]
Step-9 : Add new result -6 to the next coefficient of the dividend 7, and write down the sum 1, [ 7 + (-6)=1 ]
We have completed the table and have obtained the following coefficients 5,-5,3,2,1
Thus quotient is 5x³ - 5x² + 3x + 2 and remainder is 1.
And all these process are illustrated below.
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when students are tested and the test results are used to place them in a certain category of classes (remedial, advanced, college prep, etc.), this process is called:
Tracking is the practice of testing students and using the results to place them in specific classes (such as remedial, advanced, college prep, etc.).
What is tracking?Tracking in mathematics has become a hot topic in many school systems. By definition, tracking means that students are separated into different levels of courses due to their. mathematical ability and prior performance.The term "tracking" refers to a strategy many secondary schools employ to classify students based on their perceived aptitude, IQ, or levels of achievement. In an effort to match the curriculum and instruction to the students' needs, they are divided into high, middle, and low tracks.Tracking is the most commonly used term for ability grouping, the practice of lumping children together according to their talents in the classroom. On the elementary level, the divisions sound harmless enough: Kids are divided into the Bluebirds and Redbirds.hence,Tracking is the practice of testing students and using the results to place them in specific classes (such as remedial, advanced, college prep, etc.).
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Build a model to show 9/8 i-Ready
A model to show [tex]\frac{9}{8}[/tex] is given below.
What is an improper fraction?
When the numerator of a fraction is more than or equal to the denominator, the fraction is said to be improper. The number at the top is the numerator, and the number at the bottom is the denominator.
Given, improper fraction = [tex]\frac{9}{8}[/tex]
Now, convert the given improper fraction into a mixed fraction
i.e. [tex]\frac{9}{8} = 1\frac{1}{8}[/tex] ( mixed fraction)
That we can write [tex]1\frac{1}{8} = 1 + \frac{1}{8}[/tex]
The model to show [tex]\frac{9}{8}[/tex] is given below:
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What is the value for x when solving the equation −x (−3) = x 3 using algebra tiles? x =
The value of x found after solving the equation using algebra tiles is -3.
What is algebra tiles?
Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have demonstrated to offer solid examples.
Solving the equation for value of x
−x + (−3) = x + 3
-x -3 = x + 3
subtracting x from both sides
(-x -3) -x = (x + 3) -x
-2x -3 = 3
Adding 3 to both sides
-2x -3 + 3 = 3 + 3
-2x = 6
Dividing by 2 both side.
x = -3
Therefore the value of x = -3
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Answer:
-3
Step-by-step explanation:
A class is made up of 6 boys and 14 girls. half of the boys wear glasses. a student is selected at random from the class. what is the probability that the student is a boy with glasses? write your answer as a fraction in simplest form.
A class is made up of 6 boys and 14 girls. half of the boys wear glasses. a student is selected at random from the class.
0.2% probability that the student is a boy with glasses.
In order to calculate a probability we first need to know the total possible outcomes, so the total is boys plus the girls, 6+14=20, we have a total of 20 students, and we need the total number of successful outcomes, which is half of the girls, 4 girls use glasses.
So the probability is:
[tex]Probability = \frac{Successful Outcomes}{Total Possible outcomes}[/tex]
[tex]Probability = \frac{4}{20} \\\\Probability = \frac{1}{5} \\\\Probability = 0.2[/tex]
So the probability is 0.2% that if you pick a student at random you will pick a girl with glasses.
Hence the answer is 0.2% probability that the student is a boy with glasses.
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9. Prove that y = (x - 2)2 - 9 and y = (x + 1)(x - 5) represent the same parabola
On simplifying the given equations y = (x - 2)² - 9 and y = (x + 1)(x - 5), they represent the same parabola which is y = x² - 4x - 5
What is equation of parabola?
The equation of a parabola can be expressed in standard form and vertex form. The standard form of a parabola is y = ax² + bx + c where a, b, and c are constants, and a does not equal 0.
The vertex form of a parabola is y = a(x - h)² + k. The coordinates (h,k) represent the vertex of the parabola.
We can check if the given equations represent the same parabola by simplifying them to standard form of equation of parabola.
According to the given equation:
y = (x - 2)² - 9
y = x² - 4x + 4 - 9
∴ y = x² - 4x - 5 ------ 1)
Similarly simplifying other equation
y = (x + 1)(x - 5)
y = x² - 5x + x - 5
y = x² - 4x - 5 ----- 2)
Clearly equation 1) and 2) represent the same parabola having equation
y = x² - 4x - 5
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How did islamic scholars contribute to the growth of scientific and mathematic knowledge?.
A viable method of numeration that contained zero and allowed for the solution of equations was developed by Muslim academics, who also used logic to establish mathematical ideas and relationships.
The current arithmetic decimal system and the basic operations associated with it—addition, subtraction, multiplication, division, raising to a power, and extracting the square root and cubic root—were created by Muslim mathematicians.
The Indian numeral system, which is now known as Arabic numerals, was swiftly adopted by Islamic mathematicians. The development of algebra, the use of decimals, mathematical induction, and trigonometry were among the further contributions.
The Arabic translation of mathematical, medicinal, and astronomical writings from their original languages is one of the Islamic world's greatest contributions to contemporary science.
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Red Valley Cabs charges $4.50 to initiate a cab ride, plus an additional $3.20 per mile driven. Write an equation showing how the cost of a cab ride, y, depends on the number of miles driven, x.
Answer: y=$4.50+$3.20x
Step-by-step explanation: You already have to pay $4.50 plus $3.20 every mile driven (x) equals your final cost (y)
Which table represents a direct variation function?
Input x 3 4 5
Output y 6 10 14
Input x 1 2 3
Output y 2 4 8
Input x 4 6 8
Output y 6 9 12
Input x 1 2 3
Output y 3 9 15
Option 3 is the solution. The direct variation in this question is gotten from the option where we have the input x: 4 6 8, output y: 6 9 12
What is direct variation?In mathematics, the direct variation in the form that is
y = kx
To define the term k, k is the constant of proportionality.
The equation is written and interpreted as y is directly to x. At option 3,
y = kx
when y = 6 and x = 4, we would have 6 = 4k.
then k = 6/4
= 1.5
To confirm, we have to put the input values to see if they correspond with their y values.
1.5 x 6 = 9
1.5 x 8 = 12
Hence option 3.
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25 rules in 5 groups
There are five rules in one group
From the question, we have
25 rules in 5 groups
In one group = 25/5 = 5 rules
There are five rules in one group
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
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Help help help help help
theorem of sines answer: A
Simplify the following expression 6x^2+2x-8-7x^2
Answer:
-x^2+2x-8
Step-by-step explanation:
6x^2+2x-8-7x^2 Different features used to show like terms
Simplify =
-x^2+2x-8
Find the unit ratio.
10 to 5
As we have divided the denominator by 5, we must also divide the numerator by 5. 10 dog treats divided by 5 beagles gives us 2 dog treats per Beagle. So our Unit Rate is Unit Rate of Dog Treats per beagle is = 2:1 2:1 is a direct ratio of 10:5, they are in fact equivalent ratios.
Answer:
2:1
Step-by-step explanation:
10/5 is equal to 2/1 simplified. Therefore the simplified ratio of 10/5 is 2:1
A youth group i planning a trip to a local amuement park. They are taking a van which hold 10 people. It will cot $25 for parking and ticket to enter the park are $18 per peron. Create a table to repreent the ituation, howing the poible total cot for the variou number of people who could go?
Answer:
See below
Step-by-step explanation:
what is the correct setup to finding the slope of a line that passes through the points (6,-3),(-2,7)
Answer:
slope = - [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, - 3 ) and (x₂, y₂ ) = (- 2, 7 )
m = [tex]\frac{7-(-3)}{-2-6}[/tex] = [tex]\frac{7+3}{-8}[/tex] = [tex]\frac{10}{-8}[/tex] = - [tex]\frac{5}{4}[/tex]
The slope of a line that passes through the points (6,-3),(-2,7) is -5/4.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope of a line that passes through the points (6,-3),(-2,7):
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (7+3)/(-2-6)
m = -10/8
m = -5/4
Therefore, the slope is -5/4.
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prove that every non-empty finite set has the same number of subsets of even size as it has subsets of odd size.
It is proved that every non-empty finite set has the same number of subsets of even size as it has subsets of odd size
The set's members are numbered 1, 2, 3, 4,..., n.
There is a set with an odd number of items that corresponds to every subset with an even number of elements in the following manner:
Delete 1 from the set to create one with an odd number of elements if it is a member of the set with an even number of elements.
Add 1 to the set to create a set with an odd number of items if it isn't already a member of the set with an even number of elements.
Let's say the set has the numbers 1, 2, 3, and 4. The relationship between sets with even numbers of elements and sets with odd numbers of elements is as follows:
even odd
∅ ↔ {1}
{1,2}↔ {2}
{1,3}↔ {3}
{1,4}↔ {4}
{2,3}↔{1,2,3}
{2,4}↔{1,2,4}
{3,4}↔{1,3,4}
{1,2,3,4↔{1,2,3,4}
Therefore, it is demonstrated that any non-empty finite set has the same number of even-sized and odd-sized subsets.
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Solve the equation.
(x+3)^2-5=0
And
Solve the equation.
(2x+1)(x-5)=0
The solution to equation (x+3)² - 5 = 0 is x = -3 +√5 and x = -3 - √5. The solution to equation (2x+1)(x-5)=0 is x = -1/2 and x = 5.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
To determine the solution to equation (x+3)² - 5 = 0
(x+3)² - 5 = 0
x² + 9 + 6x - 5= 0
x²+ 6x + 4 = 0
Using the quadratic formula to solve the above quadratic function
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \:4}}{2\cdot \:1}[/tex]
[tex]\sqrt{6^2-4\cdot \:1\cdot \:4}[/tex] = 2√5
x = -6± 2√5 / 2
x = -3± √5
x = -3 +√5 and x = -3 - √5
To determine the solution to equation (2x+1)(x-5)=0
(2x+1)(x-5)=0
(2x+1) = 0 and (x-5)=0
2x = -1 and x = 5
x = -1/2 and x = 5
Thus, the solution to equation (x+3)² - 5 = 0 is x = -3 +√5 and x = -3 - √5. The solution to equation (2x+1)(x-5)=0 is x = -1/2 and x = 5.
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A set of points is shown on the graph.
Scatter plot with a point at negative 3 comma 9, a point at 0 comma 5, a point at 1 comma 8, a point at 6 comma 7, and a point at 8 comma 3.
Which of the following equations is the best model for a line of fit for the data?
y equals 2 thirds times x plus 7
y equals negative 2 thirds times x plus 7
y equals 1 third times x plus 7
y equals negative 1 third times x plus 7
Answer:
[tex]\textsf{D)} \quad y =-\dfrac{1}{3}x+7[/tex]
Step-by-step explanation:
The line of best fit of a scatter plot is a straight line that represents the general trend or pattern. It should pass as close as possible to the majority of the data points, minimizing the overall distance between the line and the points.
From observation of the given scatter plot, the line shows a negative association. Therefore, the slope of the line is negative. This means we can immediately discount the equations with positive slopes.
If we plot the line with the slope -2/3 (attachment 1 - blue line), we can see that the line passes through the first point, then has 3 points above the line but only 1 point below it. The distance between point (6, 7) and the line is much greater than the distance between the line and the other points.
If we plot the line with the slope -1/3 (attachment 2 - red line), we can see that the line passes as close as possible to the majority of the data points, and minimizes the overall distance between the line and the points.
Therefore, the equation that is the best model for the line of best fit for the data is:
[tex]y =-\dfrac{1}{3}x+7[/tex]
30/100 + 5/10
please help me.
Answer:
4/5
Step-by-step explanation:
hope it helped :)
