The solution of the radical expression ∛(4+3) will be 1.91.
What is a radical expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
The radical sign, which may be read as either the nth root of x or x radical n, expresses the root of a number. The vinculum, or horizontal line that encircles the number, and the radicand, or number beneath it, are both technical terms.
Given that the expression is ∛(4+3). The solution of the medical expression will be,
E = ∛ ( 4 + 3)
E = ∛(7)
The value of the cube root of the number 7 will be,
E = 1.91
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Find the surface area of the pyramid. The side lengths of the base are equal.
The surface area of the pyramid is 116.4 sq. ft.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
The surface area of the pyramid is calculated by adding the area of all the faces of the pyramid.
The area of the triangle is given as:
A = 1/2 (b)(h)
For the face of the pyramid:
b = 12 and h = 9
Substituting the values we have:
A = 1/2 (12)(9)
A = 54 sq. ft
The pyramid consists of three faces thus,
A = 3(54) = 162 sq ft
For the base of the pyramid:
b = 12 and h = 10.4 ft
A = 1/2(12)(10.4)
A = (6)(10.4)
A = 62.4 sq ft
The surface area of the pyramid is:
SA = 54 + 62.4
SA = 116.4 sq. ft
Hence, the surface area of the pyramid is 116.4 sq. ft.
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A bag contains 4 white marbles, 3 red marbles, and 5 blue marbles. Miko takes one marble from the bag, replaces it, and then takes another. Find P(red, then white).
Answer:
To find the probability of Miko taking a red marble first, then a white marble, we can use the formula for joint probability:
P(red, then white) = P(red) * P(white | red)
Where P(red) is the probability of Miko taking a red marble first and P(white | red) is the probability of Miko taking a white marble second, given that he took a red marble first.
P(red) = 3/12 = 1/4
P(white | red) = 4/12 = 1/3
So,
P(red, then white) = 1/4 * 1/3 = 1/12
Therefore, the probability of Miko taking a red marble first, then a white marble is 1/12.
Help solve please !!
Answer:
2+1=3, 7+8=15, 0+1=1, 8+7=15, 2+9=11, 1+3=4, 2+0=0, 4+5=9, 3+4=7
A population mean is normally distributed with a mean of 56 and a standard deviation of 12.
The mean of the sampling distribution (p) and The standard error of the mean (o) are 56 and 2 respectively.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
According to question:(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.
(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:
o = 12 / √36 = 2
(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.
This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.
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Which of the following equations represents a linear function? Please show the steps of the answer! Thank you
Answer:
2nd choice y = 1/2x - 5
Step-by-step explanation:
y = 1/2x - 5 is the only function listed that if you graph it, it makes a straight line. A linear function forms a straight line when it is plotted on a graph.
The first and last choices are number values of x.
The 3rd choice, if you graph it, makes a parabola.
Answer:
Second option:
[tex]y = \dfrac{1}{2}x -5[/tex]
Step-by-step explanation:
A linear function should have y as a function of x (or x as a function of y) and the degree of the function (the highest power has to be 1)
Both x and y must be present to make it a linear function
General slope intercept form is y = mx + b where m = slope, b = y-intercept
With these restrictions the second option is the correct one
[tex]y = \dfrac{1}{2}x -5[/tex]
This line is in slope intercept form y = mx + b where m = slope(in this case 1/2) and y-intercept b(in this cae -5)
Option 1: x = 3 is a straight vertical line parallel to the y-axis. Such a line has a slope of ∞
Option 3 is a function with degree 2 and is a quadratic function
Option 4 : 3x - 6 = 4==> 3x = 6 + 4 = 10 or x = 10/3, again another vertical line with slope = ∞
I really need help on this question. I have attached it thx. Do all the questions I have put on it so the answer and units.
Answer:
14 cm
Step-by-step explanation:
The formula for circumference of a circle is 2πr, where r is the radius. In this problem, the circumference would be 2π * 7cm = 14 cm
is the expression 3(x+2) equivalent to 3 x+6? explain
Using logarithmic properties, what is the solution to log4(y - 9) + log43 = log481? Show all necessary steps.
Answer:
y = 36
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_4(y-9)+\log_43=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log product law}}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_4\left(3(y-9)\right)=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log equality law}}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]
[tex]\implies 3(y-9)=81[/tex]
Divide both sides of the equation by 3:
[tex]\implies \dfrac{3(y-9)}{3}=\dfrac{81}{3}[/tex]
[tex]\implies y-9=27[/tex]
Add 9 to both sides of the equation:
[tex]\implies y-9+9=27+9[/tex]
[tex]\implies y=36[/tex]
Therefore, the solution to the given logarithmic equation is y = 36.
Can you please help me!!!Please
The company will be able to purchase enough pens while staying within the budget by purchasing 10 mugs only not more than that.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
A company has a budget of $305
Company needs to purchase either a mug or a pen for each of its 100 clients.
Price per Mug $5.55 Price per Pen $2.50
Now,
Price of pen = 100*2.50=250
When the number of employees are 10
=10*5.50=55.0
Mugs can be purchased
When the number of employees are 15
=15*5.50=82.5
Mugs cannot be purchased
Therefore, by algebra the answer will be 10 mugs only.
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Which is the solution of [tex]-\frac{6}{x} -\frac{x-2}{4} \ \textgreater \ \frac{3-x}{3}[/tex]?
Multiple choice question.
A)
x= −6, x= 12, or x ≠ 0
B)
−6 < x < 0 or x > 12
C)
x < −6 or x > 12
D)
−12 < x < 0 or x > 6
Answer:
C) x < −6 or x > 12----------------------
Given inequality:
- 6/x - (x - 2)/4 > (3 - x)/3Consider x ≠ 0 and multiply all terms by x, 4 and 3:
- 6*12 - 3x(x - 2) > 4x(3 - x)-72 - 3x² + 6x > 12x - 4x²4x² - 3x² + 6x - 12x - 72 > 0x² - 6x - 72 > 0 x² - 12x + 6x - 72 > 0x(x - 12) + 6(x - 12) > 0(x + 6)(x - 12) > 0The x-intercepts are:
x = - 6 and x = 12This quadratic function has a positive leading coefficient and two zeros, and hence is positive when:
x < - 6 and x > 12, the x = 0 is excluded from the given interval, therefore the above is the solution.The matching choice is C.
The median monthly rent in 1990 was $447 and $658 in 2002. What was the percent increase in the median monthly rent prices from 1990 to 2002? Round to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
Step 1: Define each variable
Let's define some variables to make the calculations easier:
t1 = the median monthly rent in 1990, which is $447
t2 = the median monthly rent in 2002, which is $658
Δ = the change in median monthly rent, which is t2 - t1
Step 2: Calculate the change in median monthly rent
Δ = t2 - t1 = $658 - $447 = $211
This means that the median monthly rent increased by $211 from 1990 to 2002.
Step 3: Divide the change by the original amount
To find the percentage increase, we need to divide the change by the original amount and multiply by 100:
Δ / t1 * 100 = ($211 / $447) * 100 = 47.2%
This means that the median monthly rent increased by 47.2% from 1990 to 2002.
Step 4: Round to the nearest tenth of a percent
The final answer is 47.2%, rounded to the nearest tenth of a percent.
The percent increase in the median monthly rent prices from 1990 to 2002 was 47.2%.
88
Stephen is comparing two mortgage options for his $80, 000 mortgage.
Mortgage A: 15 years at 4.5% with monthly payments of $611.99
Mortgage B: 30 years at 4% with monthly payments of $381.93
How much is the total payback for each mortgage option?
Provide your answer below:
Mortgage A =$
Mortgage B=$
The mortgage of A is $110158.2.
The mortgage of B is $137494.8.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Mortgage A:
15 years at 4.5% with monthly payments of $611.99.
15 years = 15 x 12 = 180 months
Total paycheck.
= 180 x 611.99
= $110158.2
Mortgage B:
30 years at 4% with monthly payments of $381.93
30 years = 360 months
Total paycheck.
= 360 x 381.93
= $137494.8
Thus,
Mortgage A = $110158.2
Mortgage B = $137494.8
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A function is given.
g(x) =
4
x + 5
; x = 0, x = h
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
A function is given net change and the average rate of change between the given values of the variable.
A. = - [tex]\frac{4h}{7h + 49}[/tex]
B. = - [tex]\frac{4}{7h + 49}[/tex]
What exactly is a sample average rate?Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.
According to given information:a) The net change is just the difference between g(h) and g(0). This is found below.
g(h) - g(0) = [tex]\frac{4}{h + 7}[/tex] - [tex]\frac{4}{0 + 7}[/tex]
= [tex]\frac{28 - 4h -28}{7h + 49}[/tex]
= - [tex]\frac{4h}{7h + 49}[/tex]
b) The average rate of change is the net change divided by the length of the interval. This is:
[tex]\frac{g(h) - g(0)}{h - 0}[/tex] = - [tex]\frac{{4h}/{7h + 49}}{h - 0}[/tex]
= - [tex]\frac{4}{7h + 49}[/tex]
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2-step Word problemas
Answer:
2) 47 snow globes (51+8-12) 23) 130 snowballs (46+59+25) 4) 92 penguins (83+69-55)
factorise 1331x³y-11y³x pls i really need it!! thank you :) !!
Answer:
11xy(121x²-y²)
Step-by-step explanation:
When factorizing, you should always look for what each term has in common.
First, let's look at the coefficients (numbers) in each term: 1331 and 11. Both are divisible by 11, so let's factorize out 11:
1331x³y-11y³x
11(121x³y-y³x)
Looking at the terms in the bracket, we see they both have 'x's in common (121x³y has three x's multiplied in and y³x has one). Let's factorize out this x:
11(121x³y-y³x)
11x(121x²y-y³)
We can also see both terms in the brackets have 'y's in common (121x²y has one y and y³ has three multiplied in). Let's factorize out this y:
11x(121x²y-y³)
11xy(121x²-y²)
Since there is nothing in common left between the terms, we can say the expression is fully factorized!
question is in the picture
The formula of the area of the trapezium as subject to x is,
x = 2A/h - y.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
The area of the trapezium,
A = (1/2)h(x + y)
To make x the subject of the equation:
2A/h = (x + y)
2A/h - y = x
x = 2A/h - y
Therefore, the formula is x = 2A/h - y.
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Mark and John work the same amount of hours babysitting and tutoring. Mark gets paid $6 per hour for babysitting and $15 an hour tutoring. He makes $150 in one week. John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114. How many hours were spent babysitting and tutoring?
The requried hours spent babysitting and tutoring are 5 and 8 hours respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the hours spent babysitting and tutoring be x and y respectively,
According to the quesiton,
Mark gets paid $6 per hour for babysitting and $15 an hour for tutoring. He makes $150 in one week.
6x + 15y = 150 - - - -(1)
John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114.
10x + 8y = 114 - - - - -(2)
Solving above equations 1 and 2 by elimination method we get x = 5 and y = 8
Thus, the requried hours spent for babysitting and tutoring are 5 and 8 hours respectively.
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help pls i will give brainliest to correct answer
The length of segment YS within the square QRST is equal to 6.
How to determine the length of a line segment within a diagonal in a square
Squares are quadrilaterals with four sides of equal length and two diagonals of equal length, in that order, diagonals QS and RT are the diagonals of square QRST. Besides, we have the following information:
VY = 13, RV = 19
The length of segment YS can be found by means of the following formula:
RV = VY + YS
YS = RV - VY
YS = 19 - 13
YS = 6
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A faucet gives 20 gallons of water in 5 seconds. How many gallons does it give in 7 seconds?
Answer:
28
Step-by-step explanation:
IF 20 GALLONS IS EQUIVALENT TO 5 SECONDS WHAT ABOUT 7 SECONDS
CROSS MULTIPLY
Answer:
20 gallons / 5 seconds = 4 gallons / second
Therefore, In 7 seconds you get (7 x 4 ) or 28 gallons.
Step-by-step explanation:
14,125 ÷ 18 = ? With a remainder
Answer:
784 R 13
Hope this helps!
Step-by-step explanation:
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75. What equation can you write to solve for x
The solution is, the value is, x = 49.6.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
given that,
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75
so, 1 + 2 = 180
or, 106 + 3x - 75 = 180
or, 3x = 149
or, x = 49.6
Hence, The solution is, the value is, x = 49.6.
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Haris Rauf is the star fast bowler for Pakistan. Harry Brook is a talented young batter of English
team. When Haris Rauf decides to bowl a yorker, 80% of the time he is able to execute the yorker
perfectly and 20% of the time it turns into a full toss. When Harry Brook faces a yorker, he hits it
for a boundary 20% of the time. When Harry Brook faces a full toss, he hits it for a boundary 90%
of the time. Haris Rauf is bowling the last ball of the innings to Harry Brook. Before running in to
bowl this last ball, Haris Rauf has decided to bowl a yorker, what is the probability that a boundary
will be scored of this last ball of the innings.
Answer:
To solve it, you need to use probability. Let me show you how.
We can use a tree diagram to represent the possible outcomes of the last ball. Here is the diagram:
```
Haris Rauf
/ \
yorker full toss
0.8 0.2
/ \ / \
boundary no boundary boundary no boundary
0.2 0.8 0.9 0.1
```
The probability of a boundary is the sum of the probabilities of the branches that end with a boundary. To find the probability of each branch, we multiply the probabilities along the branch. For example, the probability of a yorker and a boundary is 0.8 × 0.2 = 0.16.
So, the probability of a boundary is:
0.8 × 0.2 + 0.2 × 0.9 = 0.16 + 0.18 = 0.34
Therefore, the probability that a boundary will be scored of the last ball is 0.34 or 34%.
Step-by-step explanation:
Smaller metric unit to a larger unit:
6,000 grams
kilograms
6,000 grams is equivalent to 6 kilograms.
How to convert the unitsThe problem is solved by converting the given dimensions from grams to kilograms. The conversion is from a smaller metric unit to a larger metric unit.
A kilogram is a larger unit of measurement for mass or weight compared to a gram.
The prefix kilo in kilogram means 1000, so one kilogram is equal to 1000 grams.
Therefore, to convert from grams to kilograms, you simply divide the number of grams by 1000.
In this case, 6,000 grams divided by 1000 equals 6 kilograms.
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Maria is renting kayaks from a local shop that charges a $7 fee, plus an hourly rate of $5. 50. For how long can maria rent the kayak if she pays a total of $40?.
The number of hours Maria rent the kayak for the paid amount of $40 when hourly rate is $5.50 is equal to 6 hours.
Fees of renting charges paid for kayaks from a local shop = $7
Hourly rate = $5.50
Let 't' be the number of hours Maria rent kayak.
Total fees paid by Maria for renting kayak for 't' hours is equal to $40
Required equation to represents the above condition is
$40 = $7 + $5.50t
Simplify the expression to get the value of 't'
⇒ 5.50t = 40 - 7
⇒ t = 33 / 5.50
⇒ t = 6 hours
Therefore, for the number of hours Maria rent kayak by paying total of $40 is equal to 6 hours.
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Solve for x
2,4, and 6 i need help with
Answer:
2. 56°
4. 56°
For number 6, it is not shown on the photo, sorry!
Step-by-step explanation:
2. The square at the corner means that it is 90°, so 90 - 34 = 56
4. The line is straight, so it means that it is 180°, so 180 - 124 = 56
please help me ive been struggling for a little bit
Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.
What is Triangle like?It is the simplest polygon and a key component in many branches of science and mathematics.
A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.
In triangle STU, right angled at T, we have:
[tex]ST = 6UT = \sqrt{(22)}[/tex]
We can use the Pythagorean theorem to find the length of TU:
[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]
Now, we can use the definition of cosine:
cos(S) = adjacent/hypotenuse
In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:
[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]
To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):
cos(S) ≈ 0.78 (rounded to the nearest hundredth)
Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.
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WILL MARK BRAINLY IF SOMEONE CAN GIVE ME THE CORRECT ANSWER PLEASE.
The x-coordinate of P is given as follows:
x = 4.
How to obtain the x-coordinate of P?The x-coordinate of P is obtained applying the proportions in the context of this problem.
The partition ratio is 2:4, hence the equation to obtain the coordinates is given as follows:
P - A = 2/6(B - A)
P - A = 1/3(B - A).
Then the x-coordinate of P is obtained as follows:
x - 10 = 1/3(-8 - 10)
x - 10 = -6
x = 4.
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In a class of 30 students x +10 study algebra, 10+3 study statistics, 4 study both algebra and statistics. 2x study only Algebra and 3 study neither algebra nor statistics
1. Illustrate the information one a Venn diagram.
2. How many students study;
A. Algebra
B. Only statistics
1. The Venn diagrams are attached
2. When the statistics students number = 10·x + 3, we have;
The number of students that study
a. Algebra = 128/11b. Statistic = 213/11When the statistics students number = 2·x + 3, we have;
The number of students that study
a. Algebra = 16b. Statistic = 15How to solve thisThe parameters given are;
Total number of students = 30
Number of students that study algebra n(A) = x + 10Number of students that study statistics n(B) = 10·x + 3Number of student that study both algebra and statistics n(A∩B) = 4Number of student that study only algebra n(A\B) = 2·xNumber of students that study neither algebra or statistics n(A∪B)' = 3Therefore;
The number of students that study either algebra or statistics = n(A∪B)
From set theory we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 10·x + 3 - 4 = 2711·x+13 = 27 + 4 = 31=11·x = 18x = 18/11The number of students that study
a. Algebra
n(A) = 18/11 + 10 = 128/11
b. Statistic
n(B) = 213/11
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11
However, assuming n(B) = (2·x + 3), we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 2·x + 3 - 4 = 27
2·x+3 + x + 10= 27 + 4 = 31
3·x = 18
x = 6
Therefore, the number of students that study
a. Algebra
n(A) = 16
b. Statistics
n(B) = 15
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11
The Venn diagrams can be presented as follows;
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The circumference of a circle is 81.64 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer
Answer:13
Step-by-step explanation:
r = circumference/2pi
81.64/6.28 = 13
The radius of the garden is 13 units.
What is the slope of this line?
Answer: look at the image for the answer and the solution
Step-by-step explanation:
