Answer:
A radical is basically a fractional exponent and is denoted by the radical sign (√). The expression x2 means to multiply x by itself (x × x), but when you see the expression √x, you're looking for a number that, when multiplied by itself, equals x. Similarly, 3√x means a number that, when multiplied by itself twice, equals x, and so on. Just as you can multiply numbers with the same exponent, you can do the same with radicals, as long as the superscripts in front of the radical signs are the same. For example, you can multiply (√x × √x) to get √(x2), which just equals x, and (3√x × 3√x) to get 3√(x2). However, the expression (√x × 3√x) can't be simplified any further.
45 people were surveyed. 33 people like hamburgers, 18 people like hamburgers and hot dogs. How many people like hot dogs?
Answer:
12
Step-by-step explanation:
45-33 is 12
And I guess to check, make sure 12 < 18
On vacation, Tim plans to spend less than $30 a day. If he spends $12 for food, what is the greatest number of dollars he can spend per day on other things? (Express in whole dollars.) Write an inequality and solve.
Answer:
So, Tim spent maximum $ 18 dollars on other things
Step-by-step explanation:
Total spent per day is less than $ 30.
Money spent on food= $ 12
So, the maximum amount amount spent on the things is
= $ 30 - $ 12 = $ 18
So, Tim spent maximum $ 18 dollars on other things.
Simplify
[tex]\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3} +...+\frac{1}{1+2+3+...+99}[/tex]
Answer:
65/264 or 0.2462
Step-by-step explanation:
The given series is
(1/1.2.3) + (1/2.3.4) + (1/3.4.5) + ………………
If we denote the series by
u(1) + u(2) + u(3) + u(4) +……………..u(n),
where u(n) is the nth term, then
u(n) = 1/[n(n+1)(n+2)] , n = 1,2,3,4,………n.
which can be written as
u(n) = (1/2) [1/n(n+1) - 1/(n+1)(n+2)] ………………………(1)
In the question, the number of terms n =10, thereby restricting us only to first 10 terms of the series and we have to find the sum for this truncated series. Let S(10) denote the required sum. We have then from (1),
u(1) = (1/2) (1/1.2 - 1/2.3)
u(2) = (1/2) (1/2.3 - 1/3.4)
u(3) = (1/2) (1/3.4 - 1/4.5)
u(4) = (1/2) (1/4.5 - 1/5.6)
u(5) = (1/2) (1/5.6 - 1/6.7)
u(6) = (1/2) (1/6.7 - 1/7.8)
u(7) = (1/2) (1/7.8 - 1/8.9)
u(8) = (1/2) (1/8.9 - 1/9.10)
u(9) = (1/2) (1/9.10 - 1/10.11)
u(10) = (1/2) (1/10.11 - 1/11.12)
Let us now add the terms on LHS and the terms on RHS independently. The sum of LHS is nothing but the sum S(10) of the series up to 10 terms. On the RHS, alternate terms cancel and we are left with only the first and the last term. Therefore,
S(10) = (1/2) (1/1.2 - 1/11.12) = (1/2) (66–1)/132 = [65/(132.2)]
= 65/264
= 0.2462 (correct to four decimal places)
#carryonlearnig
Which step shows the result of applying the subtraction property of equality?
(12x+8)+4-3
Answer:
Value of expression = -3 / 4
Step-by-step explanation:
Given:
(12x + 8) + 4 = 3
Find:
Value of expression
Computation:
Given expression
(12x + 8) + 4 = 3
Step 1: Use Distributive property
12x + 8 + 4 = 3.
Step 2: By adding like terms.
12x + 12 = 3
Step 3: Transfer
12x = 3 - 12
Step 4: Subtract
12x = -9
Step 4: Divide both sides by 12
12x / 12 = -9 / 12
x = -3 / 4
Value of expression = -3 / 4
Because psychologists generally use college students as research participants, the research does NOT involve Group of answer choices random sampling. convenience sampling. confounds. random assignment.
Answer: random sampling
Step-by-step explanation:
Because psychologists generally use college students as research participants, the research does not involve random sampling.
Random sampling is when each sample has an equal chance of being selected. Since the psychologists are targeting a particular set of students, the random sampling might not be applicable in this case.
What calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters?
Answer:
The complete question can be found online.
The missing information is:
Carson drove a total distance of 120km, he initially has 30L of fuel on his tank, and his car efficiency is 100 cm^3/km
Remember that 1000cm^3 = 1 L
then:
100cm^3 = 0.1L
This means that he uses 0.1 L per kilometer.
The equation that shows how many liters of fuel he will have is:
initial fuel - consumed fuel.
We know that the initial fuel is 30 liters.
And the consumed fuel will be the amount of fuel he used to drive the 120 km
Remember that for each km, he consumes 0.1 L of fuel.
Then for the 120km he used 120 times 0.1 L of fuel, so he used a total of:
120*0.1 = 12 L of fuel
Then the remaining fuel in the tank is:
30 L - 12 L = 18L
There are 18 L of fuel in the tank.
Answer:
Should be 30-100/1000*120
Step-by-step explanation:
Find the vertex of the function y = (1/5)x^2 + (4/5)X + 1/5
A. (-2, 1)
B. (2, 1)
C. (2, -1)
D. 12/5, 1)
Answer:
(-2, -3/5) IS THE CORRECT ANSWER
Step-by-step explanation:
The vertex of the function y = (1/5)x² + (4/5)x + 1/5 is (-2, -3/5).
To find the vertex of the quadratic function in the form y = ax² + bx + c, we can use the formula:
x = -b / (2a)
y = f(x) = ax² + bx + c
For the given function y = (1/5)x² + (4/5)x + 1/5,
a = 1/5
b = 4/5
c = 1/5
Now we can find the x-coordinate of the vertex:
x = -b / (2a)
= -(4/5) / (2 x (1/5))
= -4/5 / (2/5)
= -4/5 x 5/2
= -4/2
= -2
To find the y-coordinate, substitute the value of x
y = (1/5)(-2)² + (4/5)(-2) + 1/5
= (1/5)(4) + (-8/5) + 1/5
= 4/5 - 8/5 + 1/5
= -3/5
Therefore, the vertex of the function y = (1/5)x² + (4/5)x + 1/5 is (-2, -3/5).
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with steps please
A student uses a clinometer to measure the angle of elevation of a sign that marks the point on a tower that is 45 m above the ground. The angle of elevation is 32° and the student holds the clinometer 1.3 m above the ground. He then measures the angle of elevation of the top of the tower as 47º. Sketch and label a diagram to represent the information in the problem. Determine the height of the tower to the nearest tenth of a metre
Answer: [tex]75\ m[/tex]
Step-by-step explanation:
Given
The tower is 45 m high and Clinometer is set at 1.3 m above the ground
From the figure, we can write
[tex]\Rightarrow \tan 32^{\circ}=\dfrac{43.7}{x}\\\\\Rightarrow x=\dfrac{43.7}{\tan 32^{\circ}}\\\\\Rightarrow x=69.93\ m[/tex]
Similarly, for [tex]\triangle ACD[/tex]
[tex]\Rightarrow \tan 47^{\circ}=\dfrac{43.7+y}{x}\\\\\Rightarrow 69.93\times \tan 47^{\circ}=43.7+y\\\\\Rightarrow 74.99=43.7+y\\\Rightarrow y=31.29\ m[/tex]
Height of the tower is [tex]43.7+31.29\approx 75\ m[/tex]
Does anyone know the answer?
Answer:
The third one
Step-by-step explanation:
f(x) = –2² – 9x
Find f(-2)
Answer:
22
Step-by-step explanation:
1.) -2²-9(-2)
2.) -2(-2)+18
3.) 4+18
4.) 22
Simplify this expression:
-(x+2)+4
i have no idea im not good with math ;(
ANSWER :
- ( x+ 2 ) + 4
-x - 2 + 4
-x + 2
Answer:
−x+2
Step-by-step explanation:
-(x+2)+4 Distribute the negative sign (-) outside of the parenthesis with x and 2 and that will turn into -x-2+4.
Add -2 and 4 and that will turn into -x+2.
If a apple cost d dollars, which of the following expressions gives the cost for 20 apples in dollars?
Answer:
$ 20d
Step-by-step explanation:
Since each Apple costs d dollars , therefore 20 will cost , $ 20d .
The correct expression that gives the cost of 20 apples, in dollars, is 20a/d. So, correct option is A.
To find the cost of 20 apples, we need to determine the expression that correctly calculates the cost based on the given variables.
Given that a represents the cost of one apple in dollars and d represents the number of dollars, we can identify the expression that calculates the cost of 20 apples.
Let's analyze each option:
A. 20a/d: This expression calculates the cost of 20 apples by multiplying the cost of one apple (a) by 20 and then dividing by d. Therefore, this expression correctly gives the cost of 20 apples in dollars.
B. 20d/a: This expression calculates the cost of 20 apples by multiplying the number of dollars (d) by 20 and then dividing by the cost of one apple (a). This does not give the correct cost of 20 apples.
C. a/20d: This expression calculates the cost of 20 apples by dividing the cost of one apple (a) by 20 and then dividing by d. This does not give the correct cost of 20 apples.
D. 20/ad: This expression calculates the cost of 20 apples by multiplying 20 by d and then dividing by the cost of one apple (a). This does not give the correct cost of 20 apples.
Therefore, the correct expression that gives the cost of 20 apples, in dollars, is A. 20a/d.
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Complete question is:
If a apples cost d dollars, which of the following expressions gives the cost of 20 apples, in dollars?
A. 20a/d
B. 20d/a
C. a/20d
D. 20/ad
A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. The stock price beyond which 0.05 of the distribution falls is _________.
Answer:
$12.43
Step-by-step explanation:
Given :
Mean = $8.52
Standard deviation, = $2.38
Stock price which falls beyond 0.05 of the distribution is at the 95th percentile
The 95th percentile distribution has a Pvalue of 1.645 (standard normal table)
We obtain the value of x, with z = 1.645
Using the Zscore relation :
Zscore = (score - mean) / standard deviation
1.645 = (score - 8.52) / 2.38
Cross multiply :
1.645 * 2.38 = score - 8.52
3.9151 = score - 8.52
Score = 8.52 + 3.9151
Score = $12.4351
Stock price beyond 0.05 is $12.43
Evaluate the function. f(x)=−x^2 −6x+12 Find f(4)
1. How to find f(4)?
I explained how to find f(5) in your previous question. It is exactly the same. We substitute x = 4 in the equation.2. Substitution and Evaluate
[tex] \large{f(4) = - {(4)}^{2} - 6(4) + 12} [/tex]
Follow BODMAS/PEMDAS rules as well! Exponent first.
[tex] \large{ f(4) = - 16 - 24 + 12} \\ \large{f(4) = - 40 + 12} \\ \large{f(4) = -2 8}[/tex]
3. Final Answer
f(4) = -28.Find the probability of rolling a three first and then a six when a pair of dice is rolled twice.
a. 1/18
b. 5/648
c. 1/54
d. 5/324
Plz help me
Answer:
5 / 648
Step-by-step explanation:
Given tbe sample space for a pair of dice attached below :
Sample space for a pair of dice = 6² = 36
Rolling a 3 first :
Recall, probability = required outcome / Total possible outcomes
P(rolling a 3). = 2 / 36 = 1 /18
Probability of rolling a 6 (second roll)
P(rolling a 6) = 5 / 36
Hence,
P(3) then P(6) ;
1 / 18 * 5/36 = 5 / 648
Which steps will verify that a parallelogram is a rectangle? Check all that apply.
To verify that a given parallelogram is a rectangle, you can calculate the lengths of all sides, and show that both pairs of opposite sides are congruent and calculate the slopes of every side, and show that adjacent sides are perpendicular.
Answer: 1st one and last one
Step-by-step explanation:
Subtract
[tex] - 3[/tex]
[tex] - {2y}^{3} [/tex]
[tex] - y[/tex]
[tex] - {5y}^{2} [/tex]
from
[tex] - {2y}^{3} [/tex]
[tex] + 4[/tex]
Answer:
Step-by-step explanation:
-2y³ + 4 - (-3 - 2y³ - y - 5y²) = -2y³ + 4 + 3 + 2y³ + y + 5y²
= -2y³ + 2y³ +5y² + y + 4 + 3 {combine like terms}
= 5y² +y + 7
Nicole invested $1600 in an account that pays 4.75% interest compounded annually Assuming no deposits or withdrawals are made, find how much money Nicole would have in the account 18 years after her initial investment. Round to the nearest tenth (if necessary ).
Answer:
2968
Step-by-step explanation:
A hatbox in the shape of a cylinder is modeled below the diameter of the cylinder is 24 inches the height of the cylinder is 8 inches what is the volume of the cylinder?
Answer:
3619.11 in³Step-by-step explanation:
Cylinder volume:
V = πr²hSubstitute values:
V = π(24/2)²*8 = 3619.11 in³As we know the,
General formula for volume of cylinder,
→ V = πr²h
Now we can find,
The volume of the cylinder,
→ πr²h
→ π(24/2)² × 8
→ π × 12² × 8
→ 3619.11 in³
Hence, volume of cylinder is 3619.11 in³.
Jordan is planning a surprise birthday
party for her brother. She would like
to invite 15 guests. She has $300.00 to
spend. Which unit rate describes her
spending for each guest?
A $15.00
B $20.00
с $25.00
D$30.00
Answer:
B. $20.00
Step-by-step explanation:
How to Evaluate9^ 1/2
Lesson name- Algebra
Answer:
ayan po answer nasa picture
Answer:
3
Step-by-step explanation:
9½=√9=3
ie. a number to the power of ½ is the same as the square root of the number
(-10)+3=10-3 true or false
Answer:
False
Step-by-step explanation:
10-3 =7
-10 + 3 = - 7
That is why this is correct
Answer:
false
Step-by-step explanation:
(-10)+3=10-3
-7 = 7
= -7≠ 7
What is the perimeter of parallelogram WXYZ? StartRoot 5 EndRoot + StartRoot 17 EndRoot units 2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units 16 units 22 units
Answer:
2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units
Step-by-step explanation:
The perimeter of the parallelogram is expressed as
Perimeter = WX + XY + YZ + WZ
Using the distance formula;
WX = √(0-(-1))²+(4-0)²
WX = √1²+4²
WX = √17
For XY:
XY = √(-2-(0))²+(3-4)²
XY = √(-2)²+(-1)²
XY = √4+1
XY = √5
For YZ:
YZ = √(-2+3))²+(3+1)²
YZ = √(1)²+(4)²
YZ = √1+16
YZ = √17
For WZ;
WZ = √(-3+1)²+(-1-0)²
WZ = √(-2)²+(-1)²
WZ = √4+1
WZ = √5
Perimeter = √17+√5+√17+√5
Perimeter = 2√17 + 2√5 units
Answer:
B
Step-by-step explanation:
HELP! Use the elimination method to solve the system of equations.
A. (0,8)
B. (-4,0)
C. (-2,4)
D. (0,3)
Answer:
B, (-4,0)
Step-by-step explanation:
2(4x - 2y = -16) 8x - 4y = -32
8x - 4y = -32
+ -3x + 4y = 12
5x = -20
x = -4
4(-4) - 2y = -16
-16 - 2y = -16
-2y = 0
y = 0
I need help plz help
answer is C. 252 ft^2
split the figure into two pieces and first figure out the rectangle (shown in turquoise).
If you multiply the width and length (18*6) you should get 108.
Then figure out the trapezoid (in magenta). the formula is (a+b)/2*h where a and b are the bases and h is the height. the bases are given, 6 and 18. to find the height, subtract the entire figure's height by 6, which is 18-6 and gives us 12. so the formula converted to this problem is (6+18)/2*12. simplify parenthesis and get 24/2*12. 24/2=12, so multiply 12*12. The area of the trapezoid is 144. Add the areas of both figures together and get 252.
Rodrigo traveled at an average speed of 55 miles per hour for 5 hours to get from one national park to the next on his vacation. What is the distance between the national parks?
Find the area of the triangle
B 2 -3 -2 -1 Use the Pythagorean theorem to find the distance between points A and B on each graph. round answers to the nearest tenth.
hypotenuse= 9²
so the distance between the 2 points is 81
4²+5²=c²
factor out the square which gives (4+5)²=c²
which makes c=9
answer=81
A triangle ABC is right angled at A, AL is perpendicular to BC. Prove that angle BAL= angle BCA.
Step-by-step explanation:
triangle BCA=BAL bcoz Angle BCA= Angle BAL
Can anyone help with this
Step-by-step explanation:
I solved it in the diagram
a) y=4.9x
b)y=63.7
c)x=13
