What is the probability of rolling a die and getting a 4 twice in a row
The probability of getting a 4 twice in a row is [tex]\bold{\frac{1}{36} }[/tex]
What is probability?"It is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
For given example,
When a die is rolled 3 times,
Total number of outcomes are,
[tex]\Rightarrow n(S) = 6^2\\\\ \Rightarrow n(S)= 36[/tex]
The probability of getting a 4 when a die is rolled is [tex]\frac{1}{6}[/tex]
[tex]\Rightarrow P(4)=\frac{1}{6}[/tex]
We want the probability of getting a 4 twice in a row.
So, the required probability is,
[tex]\Rightarrow P=P(4)\times P(4)\\\\\Rightarrow P=\frac{1}{6} \times \frac{1}{6}\\\\ \Rightarrow \bold{P=\frac{1}{36}}[/tex]
Therefore, the probability of getting a 4 twice in a row is [tex]\bold{\frac{1}{36} }[/tex]
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On the following composite figure, the longer edge length is 14 millimeters. The shorter edge length is 8 millimeters. The width of the figure, at its longest point, is 11.3 millimeters. Decompose the figure into parallelograms or triangles only. Explain or show how you decomposed the shape. Note: Lines that look parallel are parallel, and lines that look congruent are congruent.
Answer:
To decompose this shape I would draw a vertical line from the vertex that is pointing outside to the vertex that is pointing inside. By doing this the vertical line will give me 2 congruent parallelograms. Yes it's that simple
Step-by-step explanation:
Judy makes a lemon pie. Judy cuts the lemon pie into six equal pieces. Judy wants to share the pie with her friend, Edith. Judy eats one piece of the lemon pie. Edith eats one piece of the lemon pie. Judy says that each of them are one - sixth of the lemon pie. Edith says that each of them are two sixths of the lemon pie. Who Is correct?
Both Judy and Edith are correct. They each ate one-sixth of the lemon pie.
Explanation:Judy and Edith are discussing how much of the lemon pie they each ate. Judy claims that they each ate one-sixth of the pie, while Edith says they ate two-sixths. To determine who is correct, let's break it down:
Judy cut the pie into 6 equal pieces.Judy ate 1 piece, so she ate 1/6 of the pie.Edith also ate 1 piece, so she also ate 1/6 of the pie.Therefore, both Judy and Edith are correct. They each ate one-sixth of the lemon pie.
Someone help pretty please!
Mary's age is 5 times Jose's age. The sum of their ages is 18. How old is each?
Mary is 15 years old and Jose is 3 years old. This is determined by setting up a system of linear equations based on the relationship of their ages and solving for their individual ages.
Explanation:The question involves solving a system of linear equations to find the ages of Mary and Jose. Let's denote Mary's age as M and Jose's age as J. According to the problem, Mary is five times older than Jose, so we have M = 5J. Additionally, the sum of their ages is 18, which gives us a second equation: M + J = 18.
To solve for both ages, substitute the first equation into the second to get: 5J + J = 18. Combining like terms, we get 6J = 18. Dividing both sides by 6 gives us J = 3. This means Jose is 3 years old. To find Mary's age, we substitute J back into the first equation: M = 5(3), resulting in M = 15, so Mary is 15 years old.
To solve this problem, set up a system of equations where Mary's age is M and Jose's age is J. Use substitution method to solve the system. Mary is 15 years old and Jose is 3 years old.
Explanation:To solve this problem, we can set up a system of equations. Let's assume that Mary's age is M and Jose's age is J. We are given two pieces of information: 1) Mary's age is 5 times Jose's age, so we can write the equation M = 5J, and 2) the sum of their ages is 18, so we can write the equation M + J = 18.
Now we have a system of two equations with two variables:
M = 5JM + J = 18We can solve this system by substitution or elimination. Let's use the substitution method. From equation 1, we know that M = 5J. We can substitute this value of M into equation 2 and solve for J:
5J + J = 18
6J = 18
J = 3
Now that we know J, we can substitute this value into equation 1 to find M:
M = 5(3) = 15
Therefore, Mary is 15 years old and Jose is 3 years old.
Tristan’s fish is 1/2 yard long, 1/6 yard wide, 1/3 yard high. What should the side lengths of each cubic block used to find the volume be?
Answer:
The answer is 1/6 yard
Step-by-step explanation:
The length, width, and height of a cube are equal. Each cubic block must have the same length, width, and height:
Length of tank= 1/6 yard = 1/6 yard = 3 x 1/6 yard
Height of tank: 2/6 yard = 2 x 1/6 yard
width of tank= 1/6 yard
Because the length and height of the tank are multiples of the width, the length of each cubic block should be equal to the width of the tank:
= 1.6 yard
Pam asked a bank teller to cash a check for $130. The teller gave Pam a total of 9 bills. She received $10 bills and $20 bills. How many of each type of bill did Pamela receive?
The points plotted below are on the graph of a polynomial. In what range of x-values must the polynomial have a root?
Check all that apply.
A. 3 to 4
B. 5 to 6
C. 0 to 1
D. -1 to -2
E. 2 to 3
F. 1 to 2
which of the following terms- radius, chord, diameter , tangent and or secant describes the hypotenuse of a right triangle inscribed in a circle?explain your answer in complete sentences
Final answer:
The hypotenuse of a right triangle inscribed in a circle is referred to as the diameter of the circle.
Explanation:
The hypotenuse of a right triangle inscribed in a circle is referred to as the diameter of the circle.
This can be explained using the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse of the right triangle represents the diameter of the circle.
For example, if the lengths of the legs of the right triangle are represented by a and b, then the length of the hypotenuse (diameter) represented by c can be calculated as c = √(a² + b²).
The term that describes the hypotenuse of a right triangle inscribed in a circle is the diameter. This is based on Thales' theorem, which states that the hypotenuse of a right triangle inscribed in a semicircle is the diameter of the circle.
Explanation:The hypotenuse of a right triangle inscribed in a circle is described by the term diameter. When a right triangle is inscribed in a circle, the hypotenuse always corresponds to the diameter of that circle. This is because, according to the Thales' theorem, a right angle in a semicircle suggests that the side opposite the right angle of an inscribed triangle (the hypotenuse) must be the diameter of the circle. Furthermore, the relationship between the sides and the hypotenuse of a right triangle is given by the Pythagorean theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
Bryce has to complete 100 minutes of writing every ten days. He writes for 10 minutes each day. What fraction of his writing requirement does Bryce complete in five days? Write in simplest form.
A rectangular prism has a length of 412 millimeters, a width of 412 millimeters, and a height of 6 millimeters. Sally has a storage container for the prism that has a volume of 143 cubic millimeters. What is the difference between the volume of the prism and the volume of the storage container? Enter your answer in the box as a simplified mixed number or a decimal.
Answer:
21.5
Step-by-step explanation:
took test 100% 4.08 Quiz: Finding the Volume of Rectangular Prisms and Problem Solving
what is the slope of PQ is p is (-8,2) and Q is (4,2)
Which expression is equal to 5p? p + p + p + p + p 4p + 1 p + 5 p3 + p2
PLS HELP!
Part A: If (7^2)^x = 1, what is the value of x? Explain your answer.
Part B: If (7^0)^x = 1, what are the possible values of x? Explain your answer.
WILL GIVE BRAINLIEST
Which should be used to measure the length of a bookcase?
A.
thermometer
B.
tape measure
C.
clock
D.
scale
Can someone help me solve number 27?
The graph of the logarithmic function f(x) = loga(x) passes through the points and . The graph lies the y-axis.
The logarithmic graph for the function loga(x) represents relationships similar to that of a log-log plot such as exponential relationships. Understanding properties of logarithms and principles of graphing can help interpret this function. Unlike linear equations, these graphs have a unique shape that are not straight lines.
Explanation:The graph of the logarithmic function f(x) = loga(x) can be understood using logarithmic properties and graph principles. The log-log plot reveals that logarithmic graphs represent exponential relationships such as the decay of radioactivity or the relationship between light's frequency and wavelength. The logarithmic scale is advantageous in graphing large ranges of values.
There are a few principles to note about logarithms for this. For instance, the logarithm of a number with an exponent is equal to the exponent multiplied by the logarithm of the number. Similarly, the logarithm resulting from dividing two numbers is the difference between the logarithms of the two numbers. These properties can be helpful in interpreting the logarithmic graph.
Our graph, however, is not a straight line as in the case of linear equations which have a uniform slope, a y-intercept and x as the horizontal axis. Logarithmic graphs have unique characteristics determined by the base and the values of x.
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What will be the location of T in the image trapezoid
What is the volume of this object?
A)
24 mm3
B)
36 mm3
C)
48 mm3
D)
60 mm3
Answer:
(A) 24 [tex]mm^{3}[/tex]
Step-by-step explanation:
Length of the first piece = 8 - 6 = 2 mm
Width of the first piece = 1 mm
Height of the first piece = 6 mm
Volume of the first piece = 2 × 1 × 6= 12[tex]mm^{3}[/tex]
Length of the second piece = 6 mm
Width of the second piece = 1 mm
Height of the second piece = 6 - 4 = 2 mm
Volume of the first piece = 6 × 1 × 2= 12[tex]mm^{3}[/tex]
Volume of the entire solid = 12 + 12 = 24 [tex]mm^{3}[/tex]
Which one expression could represent the approximate population of the small town
Raj made this argument:
The Triangle Inequality Theorem states that if the lengths of three sides of a triangle are a, b, and c, then a + b > c. For this reason, since a, b, and c are all positive numbers, the square of a + b must be greater than the square of c. However, for a right triangle, the Pythagorean Theorem states that if the lengths of the legs are a and b, and if the length of the hypotenuse is c, then a2 + b2 = c2, not a2 + b2 > c2. Therefore, since the Pythagorean Theorem is known to be correct, and since right triangles should adhere to the Triangle Inequality Theorem, the Triangle Inequality Theorem must be incorrect.
What is wrong with Raj’s argument?
A) The square of a + b is not equal to a2 + b2.
B) One cannot assume that a, b, and c are all positive numbers.
C) It’s not true that right triangles should adhere to the Triangle Inequality Theorem.
D) It’s not true that according to the Triangle Inequality Theorem, a + b > c.
URGENT 30 POINTS! Solve. {y=x−75x+2y=7 Use the substitution method.
Here is your answer, my good sir, or maiden.
write a word phrase for the algebraic expression 2+-9
A. nine fewer than two times a number t
B. nine more than two times a number t
C. nine fewer than a number t
D. nine more than a number t
The top of a hill rises 77 ft above checkpoint 1. What is the altitude of the top of the hill? Checkpoint 1 is -173 ft above sea level.
Help me please! Given the equation 8x=4y+16 generate a plan to rewrite it in slope intercept form
An orange has about 1/4 cup of juice. How many oranges are needed to make 2 1/2 cups of juice? Select all equations that represent this question. Plz answer!
Answer:
The answer is
D (2 1/2)/(1/4)
And 10
Oranges are needed to make 2 1/2 cups of juice
Step-by-step explanation:
From the given expression
We can solve the problem
If we state it out Mathematically
Step one
1 orange will give 1/4 cup of juice
x orange will give 2 1/2 cups of juice
Step two
By cross multiplication we have
x=( 2 1/2)/(1/4)
Let's convert the mixed fraction
2 1/2
to proper fraction we have 5/2
x=( 5/2)/(1/4)
x=5/2*4/1
x=20/2
x=10
Which inequality can be used to find how many $2.50 fruit packs can be purchased for $15.00? Use f to represent fruit snacks
The inequality that can be used to find how many $2.50 fruit packs can be purchased for $15.00 is 2.50f ≤ 15, where f represents the number of fruit packs. Therefore, you can purchase up to 6 fruit packs with $15.00.
Explanation:To find how many $2.50 fruit packs can be purchased for $15.00, we can use the inequality:
2.50f ≤ 15
where f represents the number of fruit packs.
To solve the inequality, we divide both sides by 2.50:
f ≤ 6
Therefore, you can purchase up to 6 fruit packs with $15.00.
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A computer randomly selects a number from the given set. {2, 4, 6, 9, 16, 44, 51, 60, 78} What is the probability that a number less than 10 is selected? Enter your answer as a fraction, in simplest form, in the box. P(< 10) =
NEED HELP FAST PLEASE 3 Fair number cubes with sides number 1 through 6 were tossed in the air was the probability that all three cubes will land on an even number
The measure of ∠A is (12x-5)°. If x=9, find the measure of ∠A. Then classify the angle.
Given:
[tex] \angle A=(12x-5)^{\circ}\\ \\ x=9 [/tex]
Solution:
Substitute 9 for x in the expression for angle A.
[tex] \angle A=12(9) -5=108-5=103^{\circ}\\ \\ [/tex]
An obtuse angle is an angle of greater than 90° and less than 180°, so..
[tex] \angle A \; is \; equal \; to \; 103^{\circ} \; and \; it \; is \; an \; Obtuse \; Angle! [/tex]