Answer:
4 kg
Step-by-step explanation:
........................
Answer:
4 kg
Explanation:
Let the mass of tank be 't' and water 'w'
First equation : (when it is 1/4 filled with water)
[tex]\sf t + \frac{1}{4} w = 5.6[/tex]Second equation : (when it is filled fully with water)
[tex]\sf t +w = 10.4[/tex][tex]\sf w = 10.4 - t[/tex]Insert second equation into first equation :
[tex]\rightarrow \sf t + \dfrac{1}{4} (10.4 - t) = 5.6[/tex]
[tex]\rightarrow \sf t - \dfrac{1}{4} t + 2.6 = 5.6[/tex]
[tex]\rightarrow \sf \dfrac{3}{4} t = 5.6 - 2.6[/tex]
[tex]\rightarrow \sf \dfrac{3}{4} t = 3[/tex]
[tex]\rightarrow \sf t = 4[/tex]
The tank weights 4 kg when it is empty.
4. Three weeks later, you find a scooter on sale for $399.99, which reflects a discount rate of 30%.
What percentage of the original price is $399.99? Show the proportion to solve the equation.
What was the original price? (Hint, you will need to perform subtraction, similar to the
example).
Answer:
70%
$571.41
Step-by-step explanation:
100% means 1, or a whole thing.
Since the discount is 30% of the original price, and the original price is 100% of the original price, then
100% - 30% = 70%
With a 30% discount, you actually pay 70% of the original price.
$399.99 is 70% of the original price.
399.99 / 70% = x / 100%
70x = 100 × 399.99
x = 571.41
The original price was $571.41.
10% of the library books in the fiction section are worn and need replacement. 20% of the nonfiction holdings are worn. The library's holdings are 60% fiction and 40% nonfiction. The probability to get a worn book is?
Answer: 14%
Step-by-step explanation:
Let's assume that there are 100 books in total.
So there are 60 fiction books and 40 nonfiction books.
10% of 60 is 6.
20% of 40 is 8.
So there are 14 books out of 100 that are worn.
This is 14%
there are 1,500 pupils in school , 0.6 are boys how many pupils are girls
Answer:
1491 girls (99.4 percent)
Step-by-step explanation:
explanation is in the attached picture
Question 1
The total length of a hiking trail in the mountains is 8 miles. If Dale and his son completed 4/5 of the trail yesterday, how many feet did they hike?
42,240 feet
22,528 feet
11,264 feet
33,792 feet
Answer:
33, 792
Step-by-step explanation:
first convert the 8 miles to feet because our answers are in feet.
1 mile= 5280 feet
therefore 8 miles= 5280×8
= 42240
Dale and son covered 4/5 of the 42240 feet
= 4/5×42240
= 33,782 feet
Find the value of c that makes the expression a perfect square trinomial. x2 + 9 4 x + c
A) 9/16
B) 9/64
C) 81/16
D) 81/64
The value of c is 81/64 for the expression a perfect square trinomial.
What is an Expression?An expression can be defined as a mathematical statement that consists of variables, constants and mathematical operators simultaneously.
It is given that an expression
x² +9/4x +c is a perfect square polynomial
c =?
(a+b)² = a² +2ab+b²
2ab = 9/4
b = 9/8
c = b² = 81/64
Therefore the value of c is 81/64 for the expression a perfect square trinomial.
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1 x 1 x 99 x 100 hat is the awnser
Which statements are true about the ordered pair (-1,-4) and the system of equations? x-y=3 and 7x-y=-3
Answer:
when (-1, -4) is substituted into the first equation it's true
when (-1, -4) is substituted into the second equation it's true
the ordered pair (-1, -4) is a solution to the systems of equation
Step-by-step explanation:
original equation
x-y=3
multiply both sides by 7
7x-7y = 21
add 7y to both sides
7x=7y + 21
substitute into second equation
(7y+21)-y=-3
simplify
6y+21=-3
subtract 21 from both sides
6y=-24
y=-4
substitute y into original equation
x-(-4) = 3
cancel out negative signs
x+4=3
subtract -4 from both sides
x=-1
Weights of four-year-olds are Normally distributed, with a mean of 40 pounds and a standard deviation of 1.3 pounds. At his four-year checkup, Marlon’s weight is measured to be greater than 30% of boys his age. How much does Marlon weigh?
Find the z-table here.
37.6 pounds
38.4 pounds
38.7 pounds
39.3 pounds
Picture posted below
Marlon's weight is 39.3 pounds with a mean weight of 40 pounds and a standard deviation of 1.3 pounds.
We know that the formula for calculating a z-score is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Given that mean weight = 40 pounds.
and standard deviation = 1.3 pounds.
Also given that Marlon is heavier than 30% of boys his age on average, according to measurements.
The z value of 30% is -0.524.
We can put this value in the formula.
-0.524 = (x - 40)/1.3
i.e. (-0.524) * 1.3 = x - 40
i.e. - 0.6812 = x - 40
i.e. x = 40 - 0.6812 = 39.3188
Therefore, we can conclude that Marlon's weight is 39.3 pounds with a mean weight of 40 pounds and a standard deviation of 1.3 pounds. So, the last option is correct.
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urgent help needed algebra 2
The solution of the given equation 4(3x - 4) - 7( 2x + 3) = 3 is -20.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
The given equation is;
4(3x - 4) - 7( 2x + 3) = 3
To solve;
4(3x - 4) - 7( 2x + 3) = 3
Solve the parentheses using the distributive property;
12x - 16 - 14x - 21 = 3
we need to get the like terms together;
12x - 14x -16 - 21 = 3
-2x - 37 = 3
Add 37 both sides, we get;
-2x = 40
Divide both sides by -2
x = -20
Hence, the solution of the given equation is -20.
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Normal annual capacity for star company is 36,000 machine hours, with fixed factory overhead budgeted as Rs. 16,920 and an estimated variable factory overhead rate of Rs. 2.10 per hour, During October actual production required 2,700 machine hours, with a total factory overhead of Rs. 7,400. Required: Compute: 1) The applied factory overhead 2) The over-or underapplied factory overhead amount for October,
The applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
Applied and under applied factory overhead1. Applied factory overhead:
Predetermine overhead rate=Fixed overhead/Machine hours
Predetermine overhead rate=16,920/36,000
Predetermine overhead rate=0.47
Applied overhead=Machine hours×Rate
Variable=2700×2.10 per hour= $5,670
Fixed=2700×0.47 per hour=$1,269
Total overhead applied=$6,939
($5,670+$1,269)
2. Under applied overhead
Total overhead applied $6,939
Less Total factory overhead $7,400
Under applied overhead -$461
($6,939-$7,400)
Therefore the applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
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Bob has decided to make his move to his new house easier, so he is going to rent a truck to get it all moved in one trip. He is looking at two truck rental companies. U-Haul rents a 32 ft truck for $19.95 plus 49 cents per mile driven. The formula to calculate the cost with U-Haul is C = 19.95 + 0.49x, where x represents the number of miles driven. Penske rents a truck for 69 cents per mile but has no extra fees. The formula to calculate costs for Penske is C = 0.69x, where x represents miles driven. How many miles indicate that the cost of renting a truck from U-Haul is equal to the cost of renting a truck from Penske?
Which of the following demonstrates the Distributive Property?
3(4a + 2) = 12a + 6
3(4a + 2) = 12a + 2
3(4a + 2) = 4a + 6
3(4a + 2) = 7a + 5
Answer:
[tex]\fbox {3(4a + 2) = 12a + 6}[/tex]
Step-by-step explanation:
⇒ 3(4a + 2)
⇒ 3(4a) + 3(2)
⇒ 12a + 6
Answer:
A) 3(4a + 2) = 12a + 6
Step-by-step explanation:
This is the correct answer because the distributive property is where you break up all the numbers and pretty much that is what you do in A.
3 * 4a = 12a
3 * 2 = 6
So then, as you can see, the answer would be 12a + 6.
This is another explanation, even though they are LITERALLY the same.
Apply the distributive property.
3 (4a) + 3 ⋅ 2
Multiply 4 by 3.
12a + 3 ⋅ 2
Multiply 3 by 2.
12a + 6
Brainliest pls
If A=P+I make the subject as P
Answer:
[tex]P = A - I[/tex]
Step-by-step explanation:
A = P + I (Given)[tex]\implies P = A - I[/tex]Describe the end behavior for the graph of y=-x³- ax + 3, if a is a constant.
Answer: Choice C
As [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]
As [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]
Check out the diagram below.
========================================================
Explanation:
The leading term is the term with the largest exponent. That would be the term of [tex]-\text{x}^3[/tex]. The leading term directly determines the end behavior. The other terms will not play a role.
What this means is that the end behavior of [tex]\text{y} = -\text{x}^3 - \text{ax} + 3[/tex] is the exact same as the end behavior of [tex]\text{y} = -\text{x}^3[/tex]
As x gets really big in the positive direction, we'll have [tex]-\text{x}^3[/tex] get really small in the negative direction. For instance, x = 10 leads to [tex]-\text{x}^3 = -10^3 = -1000[/tex] and x = 100 leads to [tex]-\text{x}^3 = -100^3 = -1,000,000[/tex]
Therefore, as [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]
Visually the graph goes forever downward when we move to the right. We can consider this as "falls to the right".
--------------------------------
The graph "rises to the left" because as [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]
Here's a small table to give numeric examples:
[tex]\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}-1 & 1\\\cline{1-2}-10 & 1000\\\cline{1-2}-100 & 1,000,000\\\cline{1-2}\end{array}[/tex]
As x gets more negative, y becomes more positive. We have this opposite nature going on similar to the previous section.
This graph goes uphill when moving to the left.
Check out the graph below. In the diagram I used a = 2, but you could use any value of 'a' you want to get the same end behavior.
The legs of a 90-45-45 triangle are 3 and 7. What is the hypotenuse?
Answer:
The hypotenuse is [tex]\sqrt{58}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2 + 7^2 = c^2
9 + 49 = c^2
58 = c^2
Taking the square root of each side
[tex]\sqrt{58} = \sqrt{c^2}[/tex]
[tex]\sqrt{58} =c[/tex]
A water wheel is designed in the shape of a regular octagon. What is the perimeter of the water wheel?
The graph shows an eight-sided polygon. Some major points are (0, 4), (3, 3), (4, 0), (3, minus 3), (0, minus 4), (minus 3, minus 3), (minus 4, 0), and (minus 3, 3).
A.
B.
C.
D.
Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the regular octagon is 8√58 units.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
For a regular octagon, the length of each side of the octagon is the same. Therefore, the length of a single side of the octagon is,
Length of the side of the octagon = √[(-4-3)² + (0 + 3)²] = √58
Now, the perimeter of the octagon is 8 times of√58.
Perimeter = 8 ×√58 = 8√58
Hence, the perimeter of the regular octagon is 8√58 units.
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A paramedic maintains a time card for hours she works on the rescue squad. How many hours did she work per week ?
39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:
We can write a mixed fraction in a fraction:
6 1/2 = 13/2
8 1/2 = 33/2
7 3/4 = 31/4
8 1/12 = 97/12
8 5/12 = 101/12
Adding all the fractions:
[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]
[tex]=23+\dfrac{64}{4}[/tex]
= 39 hours
Thus, 39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
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help me with this please i will gave u bralinet answer who ever answer first
Answer:
[tex]\fbox {5 times}[/tex]
Step-by-step explanation:
Days where both will be done :
⇒ 2nd day × 3rd day
⇒ 6th day
Number of times in September :
⇒ The month has 30 days
⇒ Number of times = 30/6
⇒ Number of times = 5
Answer:
5 times
Step-by-step explanation:
• Calculate the lowest common multiple (LCM) of 2 and 3 to find the first day of the month in which she will do both:
LCM (2 and 3) = 2 x 3
= 6
This means, she will do both every 6th day.
• There are 30 days in September. To find how many days she will do both in September, we have to calculate how many 6-day blocks there are in 30 days:
⇒ 30 ÷ 6
= 5 times
Evaluate each expression for r=9 n t=14 enter in your numerical answer
Answer:
1764
Step-by-step explanation:
[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]
Hii!
__________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]
1764
[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]
Stick in the values: 9 for r and 14 for t, and simplify.
[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]
[tex]\bullet[/tex] Square 14 first
[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]
[tex]\bullet[/tex] Multiply the numbers
[tex]\twoheadrightarrow\sf 1764}[/tex]
[tex]\bullet[/tex] Great job! We found the answer
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
What is the solution to the equation 7(a-10)=13-2(2a+3)?
26
O a=11
O a=7
89
O a = 11
O a=621
Answer:
[tex]a = 7[/tex]
Step-by-step explanation:
[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]
Kerry has a job that pays $1,954 biweekly. How much is withheld annually for Social Security?
$82.07
$41.03
$2,113.77
$88.91
$177.81
Answer:
hi
Step-by-step explanation:
no
how do i solve this??
-6 ≤ x < -2
Step-by-step explanation:
[ => this shows ≤ sign
) => this shows < sign
3x² - 2x + 1 = [?]
x=4
Answer:
3(4)² - 2(4) + 1 = 48 - 8 +1 = 41
x = 4
[tex] {3x}^{2} - 2x + 1 \\ \\ 3 \times {4}^{2} - 2 \times 4 + 1 \\ \\ 3 \times 16 -8 + 1 \\ \\ 48 - 8 + 1 \\ \\ 41.[/tex]
An expression is shown below:
4ck2 + 10k2 − 16ck − 40k
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Part A:
The greatest common factor is 2k
2k(2ck + 5k - 8c - 20)
Part B:
factor by grouping
2k (k(2c + 5) - 4(2c + 5))2k(k - 4)(2c + 5)2k(k - 4)(2c + 5) is the final factored form
Prove Triangle ABC is congruent to Triangle CDA.
The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
What is the similarity?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In the given triangles we can see that:-
Angle BAC is congruent to Angle DCA Angle B and Angle D are congruent.The two triangles are sharing common side which is AC.Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
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Mr. Rijo bought 49 bags of soil one week and 28 bags of soil the next week. Which expression correctly applies the
distributive property to show equivalent expressions for the number of bags of soll he bought?
49 + 28 = 4(7 + 7)
59 + 28 - (7)(7) + (14)(2))
19 + 28 - (7)(14) + (7)(7)
49 + 28 - 7(7+ 4)
Answer:
49 + 28 = 7(7 + 4)
Step-by-step explanation:
49 bags of soil one week
28 bags of soil the next week
49 + 28 bags of soil purchased in total
Find the GCF (Greatest Common Factor) of 49 and 28.
49/7 = 7
28/7 = 4 (GCF is 7 since it is the largest number that can divide both 49 and 28 equally)
Factor out the GCF + rewrite division above (optional for visualization)
49/7 = 7 -> 49 = 7 * 7
28/7 = 4 -> 28 = 7 * 4
49 + 28 = 7(7 + 4)
Let me know if you have any questions!
What is the mode of 1,1,2,2,3,3,4,4
Answer: There is no mode.
Step-by-step explanation:
The mode is the number that appears the most in a given set of data. Each number in this data set is repeated twice. Therefore, there is no mode.
I hope this helped!! :)
Answer:
1, 2, 3, 4
or none
Step-by-step explanation:
Mode is the value or values in the data set that occurs most frequently.
example:
For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.
in 1, 1, 2, 2, 3, 3, 4, 4 all numbers occur the same amount of times, therefore they all (or none) are the mode
hope this helps:)
Can someone help me? I’ll give Brainliest to whoever answers correctly first
Answer:Angle C=68 degrees
Step-by-step explanation:
The solution is in the
1. Henry is working in a pack room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35
lbs. His tolerance is +/-5 lbs. Which of the following weights are allowable? Circle all allowable weights.
a. 34
b. 36
C. 29
d. 40
The allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Henry is working in a packed room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35
lbs. His tolerance is +/-5 lbs.
Weight of the bag = 35 lbs
Tolerance = ± 5 lbs
Allowable weights = 35 ± 5
= 35 + 5 = 40 lbs
= 35 - 5 = 30 lbs
Thus, the allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.
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Fine the IRQ of the data set. 11,13,9,4,6,5,8,10
PLEASE HELP!!!!!!!!!!!!!!
Answer:
5
Explanation:
Data Set : {11, 13, 9, 4, 6, 5, 8, 10}
Arrange ascendingly: {4, 5, 6, 8, 9, 10, 11, 13}
Quartiles:
Q1 --> 5.5Q2 --> 8.5Q3 --> 10.5Interquartile Range: Q3 - Q1 = 10.5 - 5.5 = 5
Proper ascending ordered set
{4,5,6,8,9,10,11,13}Q1
6+5/2=5.5Q3
11+10/2=10.5IRQ
Q3-Q1=10.5-5.5=5