The expression is simplified to -105
What is an integer?An integer can be defined as a whole number, with no fractional or decimal form which can be positive, negative or zero.
Negative integer values are the additive inverses of their corresponding positive numbers.
Integers are a collection of whole numbers and negative values.
The types of integers are;
Positive integersNegative integersZeroFrom the information given, we have;
10(-3)(4) - (-15)
expand the bracket
10(-12) - ( -15)
expand further
-120 + 15
Add the values
-105
Hence, the value is -105
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please help with 4 and 6 its my 4th time asking with no response
The solution is
a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01
b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125
The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
a)
Let the principal be P = amount after first period = $ 402
Now , the rate of interest r = 6 %
The compound interest is calculated by compounding monthly
Now , the interest for the second period = ( PRT / 100 x 12 )
Substituting the values in the equation , we get
The interest for the second period = ( 402 x 6 x 1 ) / 1200
The interest for the second period = $ 2.01
The amount after the second period = amount after first period + interest for the second period
The amount after the second period = 402 + 2.01
The amount after the second period = $ 404.01
b)
Let the principal be P = $ 18260
The rate of interest r = 2.5 %
The compound interest is calculated by compounding quarterly
Now , the interest for the first period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the first period = ( 18260 x 2.5 ) / 400
The interest for the first period = 45650 / 400
The interest for the first period = $ 114.125
The amount for the first period = 18260 + 114.125
The amount for the first period = $ 18,374.125
Now , the principal for the second period = interest + amount of first period
The principal for the second period = $ 18,374.125
The rate of interest = 2.5 %
The interest for the second period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the second period = ( 18374.125 x 2.5 ) / 400
The interest for the second period = 45935.3125 / 400
The interest for the second period = $ 114.83828125
The amount for the second period = 18,374.125+ 114.84
The amount for the second period = $ 18,488.96
Hence , the amount and interest is calculated
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Hello this is the question
Answer:
A. 36/5
Step-by-step explanation:
cross multiply
6/5 = x/6
5x = 36
x = 36/5
Answer:
A) [tex]\frac{36}{5}[/tex]
Step-by-step explanation:
[tex]\frac{6}{5}[/tex] = [tex]\frac{x}{6}[/tex] Cross multiply and solve for x
36 = 5x Divide both sides by 5
[tex]\frac{36}5}[/tex] = [tex]\frac{5x}{5}[/tex]
[tex]\frac{36}{5}[/tex] = x
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.
What are angle bisectors?Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.
According to the angle bisector theorem;
An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.
a point is equally far from both sides of an angle if it is on the angle's bisector.
According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.
The explanation with diagram is given in the image.
Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
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Find the table that follows this rule: multiply by 8 and add 5.
A.
Input 5 6 7 8 9 10
Output 40 48 56 64 72 80
B.
Input 5 6 7 8 9 10
Output 45 53 61 69 82 90
C.
Input 5 6 7 8 9 10
Output 45 53 61 59 67 75
D.
Input 5 6 7 8 9 10
Output 45 53 61 69 77 85
Answer:
D
Step-by-step explanation:
multiply by 8 and add 5.
so,
we need to do this for every unit value and see, if the result is the same as the listed output value.
5 -> 5×8 + 5 = 45
6 -> 6×8 + 5 = 53
7 -> 7×8 + 5 = 61
8 - > 8×8 + 5 = 69
9 -> 9×8 + 5 = 77
10 -> 10×8 + 5 = 85
so, D is the correct answer.
suppose a sample of a radioactive substance weighs 32 mg. one year later, the sample weighs 25.5 mg. what is the half-life of this substance? (round your answer to two decimal places.)
Solving this equation gives us a half-life of approximately 1.36 years. Rounded to two decimal places, the half-life of this substance is 1.36 years.
What is half life of the substance?The half-life of a substance is the amount of time it takes for half of the atoms in a sample of the substance to decay.
What is formula to calculate half-life?To find the half-life, you can use the following formula:
half-life = (time) * ln(2) / ln(initial mass / final mass)
half-life = (1 year) * ln(2) / ln(32 mg / 25.5 mg)
Solving this equation gives us a half-life of approximately 1.36 years.
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Question 2
What is the length of the line segment with endpoints P(2, 1,-4) and Q(-1,5,3)?
The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units
How to find the length of a line segment?To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:
length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Substituting the coordinates of P and Q into the formula, we get:
length = √((-1 - 2))² + (5 - 1))² + (3 - (-4)))² )
= √((-3))² + (4))² + (7))² )
= √(9 + 16 + 49)
= √(74)
= 8.60 units
Therefore, the length of the line segment is 8.60 units
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Shahina has 550g of apples and plenty of the other ingredients.
Can she make apple crumble for 6 people?
Explain how you got your answer.
By the way for 8 people it is:
700g of apple, 40g butter, 240g sugar and 180g flour
Shahina can make apple crumble for 6 people with 550g of apple
How to determine if she can make apple crumble for 6 people?From the question, we have the following parameters that can be used in our computation:
For 8 people it is:
700g of apple, 40g butter, 240g sugar and 180g flour
This means that the grams of apple for 1 person is
Apple unit rate = 700g of apple/Number of people
Substitute the known values in the above equation, so, we have the following representation
Apple unit rate = 700g of apple/8
For 6 people, we have the following equation
Amount = Apple unit rate * Number of people
Substitute the known values in the above equation, so, we have the following representation
Amount = 6 * 700g of apple/8
Evaluate
Amount = 525g of apple
525g of apple is less than 550g of apple
Hence, she can make apple crumble for 6 people
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Write an equation that passes through the point (4,-3) and is perpendicular to the line 4x+y=3
Answer:
y = 1/4x - 4
Step-by-step explanation:
4x + y = 3
y = -4x + 3
Perpendicular slope = 1/4
y = 1/4x + b
-3 = 1/4(4) + b
-3 = 1 + b
b = -4
y = 1/4x - 4
The probability of winning a certain game is 0. 5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?.
0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.
What is the binomial theorem on probability?The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).
When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."
The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.
Given that,
p = 0.5, So, q = 1 - 0.5 = 0.5.
If 70% of 'n' games are won then 30% of n games must be lost.
Let n = 10.
Therefore, P ( x = 3) = [tex]^{10}C_3p^7q^3[/tex]
or, P ( x = 3) = [tex]^{10}C_3(0.5)^7(0.5)^3[/tex]
or, P (x = 3) = 120×0.0078×0.125.
or, P (x = 3) = 0.117 Or 11.7% chance.
Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.
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"the time since dinosaurs became extinct is roughly equal to _____ average human lifespans"
average human lifespan: 2.4 x 10^4
time since dinosaurs became extinct: 2.4 x 10^10
The time since dinosaurs became extinct is roughly equal to 10⁶ average human lifespans
How to complete the blanks in the statementFrom the question, we have the following parameters that can be used in our computation:
Average human lifespan = 2.4 x 10^4Time since dinosaurs became extinct = 2.4 x 10^10Rewrite the exponents properly
So, we have the following representation
Average human lifespan = 2.4 x 10⁴Time since dinosaurs became extinct = 2.4 x 10¹⁰This means that
Number of times = Time since dinosaurs became extinct/Average human lifespan
Substitute the known values in the above equation, so, we have the following representation
Number of times = 2.4 x 10¹⁰/2.4 x 10⁴
Evaluate the quotient
Number of times = 10⁶
Hence, the number of times is 10⁶
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Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
[tex]51.4^{\circ}[/tex]
Step-by-step explanation:
Since this is a right triangle, the cosine formula says
[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]
[tex]\longrightarrow cos(x) = 0.6235[/tex]
[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]
Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]
14. Between a pair of points on the line y = 5x-2, suppose that the rise is 15.
Then the run is...
(A) 3
(B) 4
(C) 5
(D) 10
Answer:
Below
Step-by-step explanation:
m = slope = rise / run
m = 5 for this equation
rise /run = 5
15 / run = 5
run = 3
4. 8 friends are lining up to get in to see the Hunger Games: Catching Fire movie,
including Bob and Sam
A) What is the probability that Bob and Sam will be next to each other.
Answer:
1/64
Step-by-step explanation:
1/8 x 1/8 = 1/64
a population of adult wildebeests in a certain region of africa have weights that are normally distributed with a standard deviation of 579 lbs. how large of a sample is needed to estimate the mean weight to within 135 lbs with a 99% confidence level?
Sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
What is confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.
Z(α/2) at 99% confidence level = 2.576
λ = 579
margin of error = ( Z(α/2) * λ ) / √n = 135
(2.576 * 579) / √n = 135
On simplifying, n ≈ 123
So, sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
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one leg of a right triangle has length 24 inches; the hypotenuse is 26.7 inches. what is the length of the other leg of the triangle?
The length of the other leg of the triangle is 11.7 inches
Now, According to the question:
We have the right triangle
The length of the right triangle is 24 inches
The length of the hypotenuse is 26.7 inches
To find the length of the other leg of the triangle
We know that the Pythagorean theorem.
The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.
Let the length of the other leg of the triangle be 'x'
According to the information:
[tex]24^2 + x^2 = 26.7^2[/tex]
576 + [tex]x^{2}[/tex] = 712.89
[tex]x^{2}[/tex] = 712.89 - 576
[tex]x^{2}[/tex] = 136.89
x = [tex]\sqrt{136.89}[/tex]
x = 11.7
Hence, The length of the other leg of the triangle is 11.7 inches.
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2 ^ (x + 3) * 3 ^ (x + 4) = 18
The value of the variable x is -2
What is an algebraic expression?An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.
These expressions are also made up of arithmetic or mathematical operations, which includes;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 18
Now, let's find the factors of 18 in 2's and 3's, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2
Collect the common factors, we get;
x+ 3 + x + 4 = 1 + 2
collect like terms
2x = 3 - 7
2x = -4
make 'x' the subject of formula
x = - 2
Hence, the value is -2
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If EF = 71, FD = 80, ED = 74, IG = 40, and HG = 37, find the perimeter
of AGHI. Round your answer to the nearest tenth if necessary.
The perimeter of the object is the sum of the lengths of all the sides
which is 302 units.
What is the perimeter?Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.
In the case of a circle, we call it perimeter circumference it is the distance around the circle.
Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and
HG = 37.
Now the perimeter of this figure is the sum of the lengths of all the sides which is,
= (EF + FD + ED + IG + HG).
= (71 + 80 + 74 + 40 + 37).
= 302 units.
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need help now i need to finish this delta
Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.
What do you mean by transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
What is reflection in mathematics?In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.
Figure H
Mapped onto figure I
The required transformation:
reflection along y=x.
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Please Hurry ASAP!!!!!
The values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b
How to determine the values of the functions?We should know that in each of the functions, we have to substitute the given values
The given functions are
f(x)=3x+2
g(x)=x²-x
(14) f(x)=3x+2
Substitute for x
f(4)=3*4+2
f(x)=12+2=14
(15) f(8)=3x+2
f(8)=3*8+2
Substitute for x
f(x)=24+2 = 26
(16) f(-2)=3*-2+2
Substitute for x
f(-2)=-6+2
f(x)=-4
(17) g(2)=2²-2
Substitute for x
g(x)=4-2
g(x)=2
(18) g(-3)=3²-(-3)
Substitute for x
g(x)=9+3 = 12
(19)g(-6)=-6²-(-6)
g(x)=36+6 = 42
(20) f(2)+1
Substitute for x
=2*3+1
=6+1
=7
(21) f(1)-1
3*1-1 = 2
(22) g(2) -2
2²-2
4-2=2
23 = g(-1)+4
-1²+4
1+5=5
(24) f(x+1)
Substitute for x
= 3(x+1)+2
=3x+3+2
=3x+5
(25) g(3b)
Substitute for x
=(3b)²-3b
9b²-3b
In conclusion, the values of the values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b
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What are the domain and range of f (x) = log (x + 6) minus 4?
domain: x > –6; range: y > 4
domain: x > –6; range: all real numbers
domain: x > 6; range: y > –4
domain: x > 6; range: all real numbers
Mark this and return
Domain: x > –6; range: all real numbers are the domain and range of f (x).
What is domain and range ?
The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x).
The collection of numbers that the function assumes is known as its range. After we enter an x value, the function outputs this sequence of values.
we need to remove all the values of x such that
x + 6 ≤ 0
Solving for x, we get
x ≤ -6
So the only values of x allowed are the ones that make the next inequality true:
x > -6.
Thus we can write the domain as:
D {x | x ∈ R | x > -6}
Where the second part, x ∈ R, is usually ignored, as we assume that x is a real number .
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Answer:
2 or B
Step-by-step explanation:
The answer above is correct.
Please help me with this
the value of y is 3 when the value of x is 8.
what is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.
Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.
Given y is inversely proportional to x
When x=3, y=1/x = 8
So when x = 8 the value of y =3
Hence the value of y is 3 when the value of x is 8.
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Help please i can’t do the math right I’m not getting any of those 4 options right
Answer:
B
Step-by-step explanation:
970 + 2436 = 3406
Lindsey's Cafe uses 5 bags of coffee every day. How many days will 1/2 of a bag of coffee last?
When she uses 5 bags of coffee every day at her café, half of a bag of coffee lasts for 10 days.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. Division is a basic operation that divides an integer. It's best to imagine of it as a group of things being distributed among a group of individuals, as in the preceding example.
Here,
number of bags needed in a day=5
number of days 1/2 bag last,
=5÷1/2
=10 days
Half of bag of coffee last for 10 days when she uses 5 bags of coffee every day in her café.
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due now pls help!!!!!!!!!!!
Answer:
A and D
Step-by-step explanation:
so sorry im in school
x+y=4
-y. -y
x=4-y
4-y-y=2
4-2y=2
-4 -4
-2y= -2
/-2. /-2
y=1
x+1=4
-1 -1
x=3
so A and D is correct
Bashar drew a regular pentagon with sides that are 5 inches long. Then he drew a pentagon with sides that are half the length of the first pentagon's sides. What is the length of the sides of the second pentagon?
Answer:
The length of the sides of the second pentagon would be half of 5 inches, or 2.5 inches. This is because when you halve the length of a line, the new line is half as long as the original.
The cost of a cake is twice that of a cup of tea.
1 cake and 5 cups of tea cost £21.
How much does a cake cost?
Answer:
The cake cost $6.00
Step-by-step explanation:
Let c = the cost of the cake
Let t = the cost of the tea
c = 2t
c + 5t = 21 Substitute 2t for c
2t + 5t = 21 Combine like terms
7t = 21 Divide both sides by 7
[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]
t = 3
A cup of tea costs $3.00
c = 2t Substitute 3 for t
c = 2(3)
c = 6
A cake costs $6.00
Answer:
Cake: £6
Step-by-step explanation:
1c = 2t Eq. 1
1c + 5t = 21 Eq. 2
c = cost of a cake
t = cost of a cup of tea
Replacing Eq. 1 in Eq 2:
2t + 5t = 21
7t = 21
t = 21/7
t = 3
From Eq. 1:
c = 2t
c = 2*3
c = 6
Check:
From Eq. 2:
c + 5t = 21
6 + 5*3 = 21
6 + 15 = 21
Need to turn this in today help!!
The angle 2 is 149° , angle 3 is 31° , angle 4 is 149°
What is the name for two opposing angles?
Angles where two lines cross that are directly opposite one another are known as opposing angles. The vertex, where the lines come together to produce the angle, is the location of the junction. Vertical angles are another name for opposite angles.
Given that :
Angle 1 is = 31°
Angle 2 is = 180 - 31 = 149° (As in a line total angle is 180°)
Angle 3 is = 31° (As equal opposite angle with angle 1)
Angle 4 is = 149° (As equal opposite angle with angle 2)
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find X giving Brainly show work
Answer:
[tex]b = 6\sqrt{2}[/tex]
Step-by-step explanation:
Don't say giving brainiest for work, I will still help you.
Use the Pythagorean Theorem to solve:
[tex]a^2+b^2=c^2[/tex]
A and B refers to the legs, or the shorter sides. C refers to the hypotenuse, or the longest side.
Plug in what you know:
[tex](7)^2+b^2=(11)^2[/tex]
[tex]49 + b^2 = 121[/tex]
Subtract 49 on both sides.
[tex]49 - 49 + b^2 = 121-49[/tex]
[tex]b^2=72[/tex]
Find the square root of both sides.
[tex]\sqrt{b^2} = \sqrt{72}[/tex]
b = [tex]6\sqrt{2}[/tex]
solve the question attached
Answer:
B) y = 4a------------------------------
Given:
[tex]log_2 \ y = 2+ log_2\ x[/tex]Find y if x = a:
[tex]log_2 \ y = 2+ log_2\ a[/tex][tex]log_2 \ y =2 log_2\ 2+ log_2\ a[/tex][tex]log_2 \ y = log_2\ 2^2+ log_2\ a[/tex][tex]log_2 \ y = log_2\ 4+ log_2\ a[/tex][tex]log_2 \ y = log_2\ (4*a)[/tex][tex]log_2 \ y = log_2\ (4a)[/tex][tex]y=4a[/tex]Correct choice is B.
(3 points) assume she has brought 5 shirts and 3 jackets. for her 3-day trip (where the days are ordered), she wants to wear a different shirt and a different jacket each day. in how many ways can this be done? g
Answer:3-4 times but im not sure but here my logic
use it to your needs
Step-by-step explanation:
she has 5 shirts and 3 jackets right
so take the first shirt the third jacket then the fourth shirt the 2nd jacket
that 2 outfits then take the second shirt and the last remaining jacket then on the weekend wear one of the non-used shirts no jacket or the first jacket
-ElectricWolfieOnYT
