For the probability values - P(A) = 0.5, P(B) = 0.6, and P(A∩B) = 0.4, the values are -
a) P(A∪B) = 0.7
b) P(A∩B') = 0.2
c) P(A'∪B') = 0.6
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The given probability values are -
P(A) = 0.5
P(B) = 0.6
P(A∩B) = 0.4
a) The formula for finding P(A∪B) is -
P(A∪B) = P(A) + P(B) - P(A∩B)
Substitute the values into the equation -
P(A∪B) = 0.5 + 0.6 - 0.4
P(A∪B) = 0.11 - 0.4
P(A∪B) = 0.7
b) To find P(A∩B') use the formula -
P(A∩B') = P(B) - P(A∩B)
Substitute the values into the equation -
P(A∩B') = 0.6 - 0.4
P(A∩B') = 0.2
c) To find P(A'∪B') first find P(A'), P(B') and P(A'∩B').
P(A') = 1 - P(A)
Substitute the value -
P(A') = 1 - 0.5
P(A') = 0.5
Now, find P(B') -
P(B') = 1 - P(B)
Substitute the value -
P(B') = 1 - 0.6
P(B') = 0.4
Now, find P(A'∩B')
P(A'∩B') = 1 - P(A∩B)
Substitute the value -
P(A'∩B') = 1 - 0.7
P(A'∩B') = 0.3
The formula for finding P(A'∪B') is -
P(A'∪B') = P(A') + P(B') - P(A'∩B')
Substitute the values into the equation -
P(A'∪B') = 0.5 + 0.4 - 0.3
P(A'∪B') = 0.9 - 0.3
P(A'∪B') = 0.6
Therefore, the values are P(A∪B) = 0.7, P(A∩B') = 0.2 and P(A'∪B') = 0.6.
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If P(A) = 0.5, P(B) = 0.6, and P(A∩B) = 0.4, find (a) P(AUB), (b) P(A∩B'), and (c) P(A'U B').
Both circles have the same center. What is the area of the shaded region?
d=22 yd
yd
Use 3. 14 for. Write your answer as a whole number or a decimal rounded to the nearest
hundredth
square yards
The area of the shaded portion is area of the outer circle - area of the inner circle = 1017.36 - 379.94 = 637.42 yards²
What is Circle ?All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The following are some of the circle's crucial characteristics:
If the circles have equal radii, they are said to be congruent.The longest chord in a circle is its diameter.In the center of a circle, equal chords subtend equal angles.The chord is divided in half by the radius drawn perpendicular to the chord.Circles with various radii are comparable.A circle can encircle a kite, triangle, square, trapezium, rectangle, and more.You may encircle a square, triangle, or kite with a circle.Equal in length are the chords that are equally spaced from the center.The longest chord's (diameter) distance from the circle's center is equal to zero.As the chord length rises, the perpendicular distance from the circle's center decreases.The tangents are parallel to one another if they are drawn at the diameter's end.The radii connecting the ends of a chord to the center of a circle create an isosceles triangle.The radius of the inner circle = 22 /2 = 11 yard = r1
The distance between the inner cirle and outer circle = 7 yards
The radius of the outer circle = 18 yards = r2
The Area of the outer circle = π*r2² = 3.14 * 18² = 1017.36 yards²
The Area of the inner circle = π*r1² = 3.14 * 11² = 379.94 yards²
The area of the shaded portion is area of the outer circle - area of the inner circle = 1017.36 - 379.94 = 637.42 yards²
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rewrite the quadratic equation in factored form
Answer:
(x - 7)(x + 8)
Step-by-step explanation:
x² + x - 56
Multiples of 56 whose difference is 1: 7, 8
So, splitting the equation:
x² + 8x - 7x - 56
(x - 7)(x + 8)
The factored form of a quadratic expression is a way to rewrite the expression which shows the sums of products.
general form: [tex]y= a(x-r)(x-s)[/tex]
in which the parenthesis, when solved for will give the roots/x-intercepts of the equationwhen the a value is equal to zero:
find two numbers that sum to the middle term and when multiplied give you the product of the third term[tex]y=x^2+x-56[/tex]
find two numbers that are the sum of 1 and are the multiply to give you -56+8 and -7 create a sum of +1 and the product of -56[tex]y=(x+8)(x-7)[/tex]
What is the equation of the line described below written in slope-intercept form?
the line passing through point (2, 2) and perpendicular to the line whose equation is y = x
y = x + 4
y = -x + 4
y = x - 4
The slope of the line perpendicular to y = x is -1. The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. Substituting m = -1 and using the point (2, 2), we have:
y = -x + b
2 = -2 + b
b = 4
So the equation of the line passing through (2, 2) and perpendicular to y = x is:
y = -x + 4
Please Brainliest
El mundo cuenta con 6,974,400,000 de personas y si la población mundial aumenta en un 1. 2% anualmente ¿Cuántas personas aumentan en un año?
The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 7,058,092,800
What is percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
By dividing the value by the entire value and multiplying the result by 100, one may get the percentage. The percentage calculation formula is (value/total value)100%.
The word "percentage" means "out of 100." In mathematics, percentages are used, together with fractions and decimals, to denote parts of a whole. The total is split into 100 equal pieces to calculate percentages.
Total population of the world is 6,974,400,000
The population is incresing at a 1.2% rate annually
The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 6,974,400,000 + 836928000 = 7,058,092,800
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Mr. Cortez is building a brick boarder the bricks are 1 ft. How many bricks does he need to buy? Use 3.14 for pi
The number of bricks needed to border the circular pool is 6.28r.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
Given, Mr. Cortez is putting a brick border around his circular pool.
So, He is boarding the circumference of the circular pool which has a distance of 2πr.
Now, The bricks are 1 foot in length.
Therefore, The number of bricks needed is,
= 2πr/1.
= 2πr.
= 6.28r.
According to the radius number of bricks can be determined.
Q. Mr. Cortez is putting a brick border around his circular pool. The bricks are 1 foot in length. How many bricks does Mr. Cortez need to buy to build the border? Use 3.14 for π.
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Circles equations and coordinates
Desperate help!!!!
The complete coordinates are (8, 0), (0, -8), (-8, 0) and (0, 8)
How to determine the corodinatesFrom the question, we have the following parameters that can be used in our computation:
x^2 + y^2 = 64
The above is the equation of a circle
Express 64 as 8^2
So, we have
x^2 + y^2 = 8^2
When y = 0, the possible values of x are
x = -8 and x = 8
When x = 0, the possible values of y are
y = -8 and y = 8
This means that the complete coordinates are (8, 0), (0, -8), (-8, 0) and (0, 8)
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In ΔFGH, f= 8.8 inches, m∠F=23° and m∠G=107°. Find the length of g to the nearest 10th of an inch
The value of length g is 21.56 inches
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Therefore to find length g
f/sinF = g/sinG
8.8/sin23 = g/sin 107
8.8 × sin107 = g× sin 23
8.8 × 0.956 = g × 0.39
g = 8.8 × 0.956/0.39
g = 8.41/0.39
g = 21.56 inches
therefore the value of the length of g is 21.56 inches
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Answer:21.5
Step-by-step explanation:
earth is approximately a sphere of radius 6.37 x 10 6 m. what are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers?
(a) Circumference of Earth in kilometers: 40,075.017 km
(b) Surface area of Earth in square kilometers: 510.1 million km^2
(c) Volume of Earth in cubic kilometers: 1.08 trillion km^3
To calculate these values, we use mathematical formulas that relate to the sphere shape of the Earth.
For (a), we use the formula for the circumference of a circle, C = 2 * pi * r, where r is the radius of the Earth in meters (6.37 x 10^6 m). We then convert this result to kilometers by dividing by 1000.
For (b), we use the formula for the surface area of a sphere, A = 4 * pi * r^2, where r is the radius of the Earth. Again, we convert this result to square kilometers.
For (c), we use the formula for the volume of a sphere, V = (4/3) * pi * r^3, where r is the radius of the Earth. We then convert this result to cubic kilometers by dividing by 10^9.
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let a . find the third column of without computing the other two columns.
The third column of the matrix is:
[tex]\begin{bmatrix}1 \\5 \\7\end{bmatrix}[/tex]
The third column of a matrix can be calculated without computing the other two columns by using the formula:
A_{ij} = (A_{i1} - A_{i2}) \times \frac{j - 1}{2} + A_{i2}
Where A_{ij} is the element in the ith row and jth column of the matrix, A_{i1} is the element in the ith row and 1st column of the matrix and A_{i2} is the element in the ith row and 2nd column of the matrix.
To calculate the third column of a matrix, we will first calculate the difference between the first two columns. For example, if we have the following matrix:
[tex]\begin{bmatrix}1 & 4 & ? \\7 & 2 & ? \\3 & 8 & ?\end{bmatrix}[/tex]
The difference between the first two columns is 3 (4 - 1 = 3). Now we can use the formula to calculate the third column. For the first row, we have A_{11} = 1, A_{12} = 4, and j = 3 (the third column). Plugging these values into the formula, we get:
A_{13} = (1 - 4) \times \frac{3 - 1}{2} + 4 = 1
For the second row, we have A_{21} = 7, A_{22} = 2, and j = 3 (the third column). Plugging these values into the formula, we get:
A_{23} = (7 - 2) \times \frac{3 - 1}{2} + 2 = 5
For the third row, we have A_{31} = 3, A_{32} = 8, and j = 3 (the third column). Plugging these values into the formula, we get:
A_{33} = (3 - 8) \times \frac{3 - 1}{2} + 8 = 7
Therefore, the third column of the matrix is:
[tex]\begin{bmatrix}1 \\5 \\7\end{bmatrix}[/tex]
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22 VA-Geometry IC (Year)
Determining Truth Values
Suppose statement p is true but statement q is false. Which of these compound statements are true? Check all that
apply.
О р^g
Opvq
Op-q
9-P
Op-q
q-p
If statement p is true but statement q is false, then the following compound statements are true -
Option B: p ∨ q
Option D: q → p
What is compound statement?
A compound statement is a collection of two or more statements joined together using terms like "or," "and," "if then," and "only if." Each component statement of a compound statement can be determined to be true or untrue with clarity.
If the truth value of the statement p is 'True' and truth value of statement q is 'False',
p ∧ q → False [Conjunction of both the statements will be true only when both the statements are True]
p ∨ q → True [Disjunction of two statements will be false only when both the statements are false]
(p → q) → False [p is same as q]
(q → p) → True [Implication of both the statements is false only when p is true and q is false otherwise true]
(p ↔ q) → False [Bi-conditional statements are true if and only when both the statements are true]
(q ↔ p) → False [Bi-conditional statements are true if and only when both the statements are true]
Therefore, the compound statements p ∨ q and (q → p) is true.
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A class used cars(x) and vans(y) to go on a field trip. They used 11 cars and vans. Each car holds 5 students and each van holds 8. If 73 students went on the trip then how many of each vehicle did the class use.
Answer:
X=5 Cars
Y=6 Vans
Step-by-step explanation:
Let's assume the number of cars used is x and the number of vans used is y.
We can set up two equations based on the information given:
x + y = 11 (the total number of vehicles used)
5x + 8y = 73 (the total number of students that went on the trip)
We can use substitution to solve for one of the variables in terms of the other:
y = 11 - x
5x + 8(11 - x) = 73
5x + 88 - 8x = 73
-3x = -15
x = 5
So the class used 5 cars and 11 - 5 = 6 vans.
A survey of statistics undergraduate at prosperity university completed a survey that asked for their verbal and math sat scores. They wanted to predict the verbal score based on the math score. The value of r-squared was 12. 78%. The least squares regression equation is yhat = 383. 3 + 0. 3489x. Find r.
The coefficient of determination (r-squared) provides an indication of how well the regression model fits the data and the value of r is 0.3574
In this example, the r-squared value is 12.78%, which means that 12.78% of the variation in verbal SAT scores can be explained by the variation in math SAT scores. The least squares regression equation is yhat = 383.3 + 0.3489x, where yhat is the predicted verbal score and x is the math score.
The coefficient of correlation (r) provides a measure of the strength of the linear relationship between two variables. In this example, the coefficient of correlation (r) can be calculated from the coefficient of determination (r-squared) as follows: r = √r-squared = √12.78% = 0.3574. This indicates that there is a weak linear relationship between verbal and math SAT scores.
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solve for
secx = 1 - tanx
The required solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
sec(x) = 1 - tan(x)
1/cosx = cosx - sinx / cosx [secx = 1 / cosx ; tanx = sinx / cosx]
cosx = 1 + sinx
1 + sinx - cosx = 0
1 + √2[sin{x - π/4}] = 0
sin{x - π/4} = -1/√2
x - π/4 = 5π/4 + 2nπ
x = 3π/2 + 2nπ
Thus, the solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.
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In Activity 1. 3
For the second set of values：
a. Which among the missing components can be solved using the given？
b. How will you solve the next missing component？
The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides
a. The missing components that can be solved using the given values are the missing sides of the triangle (side b and side c).
b. To find the missing side, we can use the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the two sides of the triangle, and c is the hypotenuse. Therefore, we can solve for c by taking the square root of (a^2 + b^2).
The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides. To do this, we take the square root of the sum of the squares of the two given sides, which gives us the length of the hypotenuse.
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You decide to invest in government bonds to save money for your eventual wedding. You have an
initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate
of return. What will be the value of your investment at maturity?
y = a(1+r)²
Round off to the nearest whole number
(don't forget to change your rate to a decimal percentage)
The value of your investment at maturity at a 10% rate of return will be,
$8470.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, An initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate of return.
We know, 10% = 10/100 = 0.1.
Therefore, The value of your investment at maturity will be,
y = 7000(1 + 0.1)².
y = 7000(1.1)².
y = 7000×1.21.
y = 8470.
So, The value of the maturity will be $8470.
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PLEASE HELP ME !! I WILL GIVE A LOT OF POINTS
The value of the integral expression is -1/2ln(9)
How to evaluate the integralFrom the question, we have the following parameters that can be used in our computation:
Integral of 4/(9 - 8x) from 2 to 9
Using a graphing calculator as a guide, we have the following:
Integrand = -ln(|8x - 9|)/2 from 2 to 9
Substitute the known values in the above equation, so, we have the following representation
Integrand = -ln(|8 * 9 - 9|)/2 + ln(|8 * 2 - 9|)/2
Evaluate
Integrand = -1/2(ln(63/7)
Evaluate the quotient
Integrand = -1/2ln(9)
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Bernard borrows a sum of money from the bank which charges a compound interest of 4. 2% per annum, compounded quarterly. Given that Bernard had to pay $96. 60 in interest payments at the end of the first year, find the original sum of money borrowed, giving your answer correct to the nearest dollar.
(answer : $2264 )
The original sum of money borrowed would be $ 2246.51.
What is meant by Future Value?A financial concept called future value (FV) determines the worth of an asset by using projected factors like future interest rates or cashflows. An investor could find it interesting to know how much, given a projected rate of return, their investment might be in five years. Future value is the idea that an investment will be worth more in the future if its current value is multiplied by anticipated growth.
Interest = $ 96.60
Interest is compounded 6 times in a year; n = 6
time = 1 year ; Rate of interest (r) = 4.2 %
Interest = Future Value - Principal Value
Future Value = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}$[/tex]
Substituting this value in equation (1), We get
Interest = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}-$[/tex]Principal
96.60 = Principal [tex]$\left[\cdot\left(1+\frac{4.2}{100 \times 6}\right)^{6 \cdot 1}-1\right]$[/tex]
Principal = $ 2246.51
Therefore, the original sum of money borrowed would be $ 2246.51.
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Line m and line n are parallel.
Which is the value of x?
Responses
x=15
x = 15
x=12.5
x = 12 . 5
x=7.5
x = 7 . 5
x=2
x = 2
If line m and n are parallel, the value of x is determined as 10.
What is the value of x?The value of x is determined by applying the following rules of parallel lines as shown below.
The corresponding angles of the parallel lines are equal,
the corresponding angles are given as;
8x + 50 = 130
now solve for x, by making x the subject of the formula.
8x = 130 - 50
8x = 80
divide through by 8
8x / 8 = 80 / 8
x = 10
Thus, the value of x is function of the corresponding angles.
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Apply the distributive property to factor out the greatest common factor. 24+18t =24+18t=24, plus, 18, t, equals.
The distributive property to factor out the greatest factor 24+18t is 6(4+3t).
The distributive property to factor out the greatest common factor 24+18t.
The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation. This property can be stated symbolically as:
A ( B+ C) = AB + ACWell, some of the common factors that 24 and 18 shares are 2, 3, and 6.
The greatest factor is 6.
⇒ [tex]\frac{24}{6}[/tex]=4
⇒ [tex]\frac{18t}{6}[/tex]=3
Because 6x4=24 and 6 x 3t= 18t
Therefore, the distributive property to factor out the greatest factor 24+18t is 6(4+3t).
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Find the missing length. The triangles in each pair are similar.
Answer:
1) 117
2) 24
Step-by-step explanation:
Corresponding sides are in the same ratio for similar triangles
1)
For triangles MUL and WUV:
UW/UM = UV/UL
?/45 = 104/40
? = 45 x 104/40 = 117
2)
For triangles RST and RKH
RS/RK = RT/RJ
?/12 = 20/10 = 2
? = 2 x 12 = 24
the base of is the parabolic region {(,)|2≤≤1}. cross-sections perpendicular to the -axis are squares.
The volume of the solid is 0 cubic units.
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.
The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
The volume of the solid is given by the definite integral:
V = ∫_[tex]{y=2}^{1} A(y) dy[/tex]
Where A(y) is the area of the cross-section at y. Since the cross-sections are squares, we know that A(y) = [tex]y^{2}[/tex].
So, the volume is given by:
V = ∫_[tex]{y=2}^{1} y^{2} dy = [\frac{y^{3} }{3} ]_{y=2}^{y=1} = (\frac{8}{3} - (\frac{2^{3} }{3}= (\frac{8}{3}-\frac{8}{3} ) =0[/tex]
The volume of the solid is 0 cubic units.
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Which shape has only acute angles?
Answer: Acute Triangles
Find the measure of each interior angle of the regular polygon. 7th
The measure of each interior angle of the regular polygon is equal to 150°.
What is a regular polygon?In Euclidean geometry, a regular polygon simply refers to a form of polygon which has all of its sides and interior angles being equal.
In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Where:
n represents the number of sides of a regular polygon.
Similarly, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:
Interior angles = [180 × (n - 2)]/n
Interior angles = [180 × (12 - 2)]/12
Interior angles = 180 × (10)/12
Interior angles = 1800/12
Interior angles = 150°
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1. (10 pts) use the definition of big o notation to find the constants c, no which show that t(n) is o(f(n)). a. ()= 32 4, ()= 52
use the definition of big o notation to find the constants c, no which show that t(n) is o(f(n)) then 5^n+25 is not = 5^n
The main purpose of the computational complexity is to categorize the algorithms about their show. And we can represent the T(n), which is the time function with the help of the big O notation, for showcasing an algorithm runtime complexity. As an example,
T(n) = O(n3)
proves that the algorithm has the cubic time complexity.
Now let's define Bio O, and from here we will get our answer. For any function which is monotonic in nature, f(n) and g(n) from the +ve integers to the +ve integers, we assume that f(n)= O(g(n)) when exist a c>0 which is the constant, and n0 greater than 0, such that
f(n) < c * g(n), for each n>=n0
i) if O (5^n)= 4^n + 25
O (f) should be = (20^n)/f + 25
Then constant
O(5^n)= (20^n)/(5^n) + 25 = (20/5)^n +25=4^n+25
ii) O (4^n)=(20^n)/(4^n) + 25 = (20/4)^n +25=5^n+25
And 5^n+25 is not = 5^n
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complete question is
Use the definition of O (f) to show that 4^n + 25 is O (5^n) (ii) show that 5^n is not O (4^n)
How can the study of mathematical logic help you in your everyday life?
The study of mathematical logic help you in your everyday life in the following way.
Mathematical logic is a branch of mathematics that deals with the principles of reasoning and makes statements based on deductive reasoning.
It is not just a subject that helps you ace your math exams but also a useful tool in your everyday life.
Understanding the basic principles of logic can help you make better decisions, solve problems more effectively, and communicate your ideas more clearly.
Logic helps you analyze information, evaluate arguments and make informed decisions.
In everyday life, you often encounter situations where you have to make choices based on information that is incomplete or ambiguous.
Furthermore, logic can also help you improve your critical thinking skills. By understanding how to reason and argue logically, you can more easily identify and evaluate flawed arguments, understand the relationships between different ideas and reach more accurate conclusions.
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how is calculus used in disasters
Answer: quantifies the economic devastation of natural and man-made disasters
2 c −3 d 6 tart fraction, c, divided by, 2, end fraction, minu, 3, plu, tart fraction, 6, divided by, d, end fraction when c=14c=14c, equal, 14 and d=3d=3
2/5th of a number is 40% of that number.
In order to calculate the percentage of a given number that is equal to 2/5 of that number, we must first convert the fraction to percentage form, which is as follows:
= 2/3 * 100
= 0.4 * 100
= 40%
We will use the following example to validate the aforementioned process:
Assume that it is 50.
First, 2/5 of 50 equals 2/5 * 50, or 20.
Second, 40% of 50 equals 40/100 * 50 = 0.4 * 50 = 20.
The equality of the two results is evident.
2/5 of a number is therefore 40% of that number.
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The question is incomplete;
\dfrac25 start fraction, 2, divided by, 5, end fraction of a number is what percentage of that number?
Joey earns $12 an hour. Blake earns $16 per hour. Joey receives a raise of $1. 50 every six months, and Blake receives a raise of $0. 50 every six months. Which equation can be used to find x, the number of six month intervals it will take Joey to earn hourly the same as Blake?
Therefore, in order for Joey to earn the same hourly wage as Blake, she will have to labor for 8 six-month periods or 4 years.
We'll refer to the quantity of six-month intervals as x. Blake's hourly wage can be represented as 16 + 0.50x, and Joey's hourly wage may be represented as 12 + 1.50x after x intervals. We may set the two expressions equal to one another and solve for x to determine when Joey's salary will match Blake's salary:
12 + 1.50x = 16 + 0.50x \s0.50x = 4 \sx = 8
Joey will therefore need to work for 8 six-month periods, or 4 years, in order to make the same hourly rate as Blake.
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Tell which equation you would choose to solve for one of the variables when solving the system by substitution. Then solve the system by substitution.
Equation 1: 2x − 3y = 11
Equation 2: x + 2y = −5
PLEASE I REALLY NEED HELP RIGHT NOW, IM IN A CRISIS! I WILL MARK THE BRANLIEST I SWEAR!!!!
The equation we will use is Equation 1: 2x − 3y = 11. The values of x and y are 1 and -3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
Equation 1: 2x − 3y = 11
Equation 2: x + 2y = −5
Now,
Equation 2: x + 2y = −5
x=-5-2y
Substituting the value of x in equation 1
2(-5-2y)-3y=11
-10-4y-3y=11
-10-7y=11
-7y=11+10
-7y=21
y=-3
Substituting the value of y in equation 2
x+2*-3=-5
x=-5+6
x=1
Therefore, the solution of the system of equations will be x=1,y=-3
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GRAPHING EXPONENTIAL FUNCTIONS
Please show work I don’t understand how to do this
Solving the provided question, we can say that the given exponent is
[tex]32 = 2^{ 3x - 1 }[/tex] => 64 = [tex]2^{3x}[/tex] => [tex]2^{3(2)} = 2^{3x}[/tex] on comparing both side, we have x = 2
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
the given exponent is
[tex]32 = 2^{ 3x - 1 }[/tex]
64 = [tex]2^{3x}[/tex]
[tex]2^{3(2)} = 2^{3x}[/tex]
on comparing both side, we have
x = 2
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