To solve the equation 1 3/5(t-6)=-0.4, first distribute 1 3/5 to the terms inside the parentheses. Then, multiply both sides of the equation by the reciprocal of 8/5 to isolate the variable t. Finally, simplify the equation to find the solution t = 5.75.
Explanation:To solve the equation 1 3/5(t-6)=-0.4, we can follow these steps:
Distribute 1 3/5 to the terms inside the parentheses. This gives us 8/5(t-6)=-0.4.Multiply both sides of the equation by the reciprocal of 8/5, which is 5/8, to cancel out the coefficient on the variable. This gives us t-6 = -0.4 * 5/8.Simplify the equation by multiplying and dividing as necessary. This gives us t-6 = -0.25.Add 6 to both sides of the equation to isolate the variable t. This gives us t = -0.25 + 6.Simplify the equation to find the final solution. This gives us t = 5.75.Therefore, the solution to the equation is t = 5.75.
Final answer:
To solve the equation 1 3/5(t-6)=-0.4, distribute the 1 3/5 first and then simplify the equation by adding and subtracting terms to isolate t. The final solution is t = 2.
Explanation:
To solve the equation 1 3/5(t-6)=-0.4, we can begin by distributing the 1 3/5 to the terms inside the parentheses:
1 3/5(t-6) = 1 3/5 * t - 1 3/5 * 6 = 8/5t - 18/5
Now, we can rewrite the equation as:
8/5t - 18/5 = -0.4
Next, we can get rid of the fraction by multiplying both sides of the equation by 5:
5(8/5t - 18/5) = 5(-0.4)
After simplifying, we get:
8t - 18 = -2
Now, add 18 to both sides of the equation:
8t - 18 + 18 = -2 + 18
Simplifying further, we have:
8t = 16
Finally, divide both sides of the equation by 8 to solve for t:
t = 16/8
Therefore, the solution to the equation is t = 2.
I don't know math can u help me please
Angles are suck
Answer:
M<FDE = 360 degrees
Step-by-step explanation:
120 degrees is supplementary to x which makes it 120. 120+120=240 degrees. angle x and angle d = 120+120 which makes it 360 degrees.
M<ADE however, is 110+120=280, 360-280=80 degrees which is 110+120+80=360 degrees. So, M<ADE is 360 degrees and it is equal to M<FDE which is also 360 degrees.
All of them are equal. The sum of the figure is 720 Degrees.
Answer:
∠FDE = 130°
Step-by-step explanation:
Since BC and DE are parallel lines, then
∠BDE = ∠ABC = 110° ( corresponding angles are congruent )
The sum of the angles round a point = 360°, thus
∠BDE + ∠BDF + ∠FDE = 360 , hence
110 + 120 + x = 360
230 + x = 360 ( subtract 230 from both sides )
x = 130
Hence x = ∠FDE = 130°
What is the measure of a
70º
It's a supplementary angle so 180º - 110º
Answer:
a = 70
b=60
Step-by-step explanation:
Angle a and 110 are supplementary, which means they add to 180 degrees
a+ 110 = 180
Subtract 110 from each side
a+110-100=180-110
a = 70
The three angles of a triangle add to 180
a+ b+ 50 = 180
We know a = 70
70 + b + 50 = 180
120 + b = 180
Subtract 120 from each side
120-120 + b = 180-120
b = 60
Jacob is tasked with the duty of selecting one name from a list of all employees in his company to award him or her and his or her family an all-expenses-paid trip to Canada. After selecting a name from a drum with all employee names in it, the lucky winner is Sally from recruiting. What kind of sampling is this?
Stratified random sampling
Systematic sampling
Simple random sampling
Convenience sampling
Answer:
I think it is C. If im wrong, then it is A because I know that it is random sampling.
Step-by-step explanation:
Answer:
C: Simple Random Sampling
39/51 change to lowest terms
Answer:
As a proper fraction - 39/51 = 13/17
As a decimal number: 39/51 ≈ 0.76
As a percentage: 39/51 ≈ 76.47%
Step-by-step explanation:
Calculate the greatest (highest) common factor (divisor), gcf (gcd).
13/17 =
13 ÷ 17 =
0.764705882353 ≈
0.76
By precentage
0.764705882353 =
0.764705882353 × 100/100 =
76.470588235294/100 =
76.470588235294% ≈
76.47%
A painter needs a piece of glass to protect a painting. He is also putting wooden strips around the perimeter to make a frame for the painting. The painting is 85 centimeters by 62 centimeters. How many square centimeters of glass does he need to cover the area of the painting?
Answer:
5270cm^2
Step-by-step explanation:
85 * 62 = 5270
It says it is asking for square centimeters and area, so use the formula for the area of a rectangle (b * h).
Answer: 5270cm^2
Step-by-step explanation: 85 * 62 = 5270
Use the figure below to find the long leg Help plzzz
Answer: The answer is 7√3
Step-by-step explanation:
Since the hypotenuse is twice as long as the shortest leg and the triangle is 30°-60°-90°, therefore the shortest leg is 7 (not the answer to your question) and the other leg is 7√3. I hope this helps :)
Answer:
D. 7√3Step-by-step explanation:
I just did this question and this was the answer that was right for me :) Hope this helps!
Write down the nth term of the following sequence:
7 2 -3 -8 -13
With steps and explanation please,!!
Answer:
see explanation
Step-by-step explanation:
This is an arithmetic sequence with n th term
• [tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
d = 2 - 7 = - 3 - 2 = - 5 and a = 7, hence
[tex]a_{n}[/tex] = 7 - 5(n - 1) = 7 - 5n + 5 = 12 - 5n
[tex]a_{n}[/tex] = 12 - 5n ← n th term formula
Kira's Bagel Shop recently sold 18 bagels, of which 6 were blueberry bagels. What is the experimental probability that the next bagel sold will be a blueberry bagel?
108 is the number of blueberry baglels
A company needs 713 slices of pizza for a company party. If each pizza is cut into 8 slices, about how many whole pizzas should the company order? A) 60 B) 70 C) 80 D) 90
Answer:
D
Step-by-step explanation:
To find the number of WHOLE pizzas needed, we need to divide the total number of slices needed (713) by 8 slices. Thus
[tex]\frac{713}{8}=89.125[/tex]
because we can't order fractional pizza, we need to round up. So we will need 90 pizzas.
Correct answer is D.
Please help!! also please explain I would like to understand.
Answer:
A
Step-by-step explanation:
First, put this equation in slope intercept form.
[tex]y=mx+b[/tex]
Where m is the slope and b is the y intercept.
[tex]y+1>2(x-1) \\ \\ y+1>2x-2 \\ \\ y>2x-3[/tex]
Since it's greater than, the solution set is above the line, effectively eliminating graph D.
Now we should graph it.
We can see that the point [tex](2,1)[/tex] is on the graph, and only Graph A has that point. Therefore, Graph A is the correct graph.
Answer:
A
Step-by-step explanation:
We can simply treat the inequality like an equation because the numbers are on the line. That is y + 1 = 2(x - 1).
Then, we can plug in some numbers:
If x = 2: y + 1 = 2(2 - 1)
y + 1 = 2
y = 1
So one point on the line is (2, 1). B, C, and D don't work because it is impossible for this point to be on the line; the x coordinate corresponds to another y-coordinate, or vise-versa ((3, 1), (2, 0) and (3, 1), respectively) . Therefore, the correct answer is A.
Figure 1 is a square pyramid. Figure 2 is a right triangular prism.
Complete the following statement about Figures 1 and 2.
The surface area of Figure 1 is ___ square centimeters ___ than the surface area of Figure 2.
Answer:
the answer is
The surface area of Figure 1 is 10.2 square centimeters Less than the surface area of Figure 2.
Step-by-step explanation:
Figure 1
area of a square = s2
=9squared
=81 sq cm
area of triangle = 1/2 bh
=1/2 (9cm) (14cm)
=63 sq. cm
find surface area
SA = 81 sq. cm + 4(63 sq. cm)
SA = 81 sq. cm + 252 sq. cm
SA = 333 sq. cm
Figure 2 Calculation
area of rectangle = lw
a = (12cm) (8 cm)
a = 96 sq. cm
area of triangle = 1/2 bh
=1/2 (8 cm) (6.9 cm)
= 27.6 sq. cm
total surface are of figure 2
SA = 3 (96 sq.cm) + 2 (27.6 sq. cm)
SA = 288 sq. cm + 55.2 sq. cm
SA = 343.2 sq. cm
find the difference between figure 1 and figure 2
343.2 sq. cm - 333 sq. cm = 10.2 sq. cm
Final answer:
We cannot complete the statement definitively about the surface area comparison between the square pyramid and the triangular prism without specific measurements. However, if we knew the dimensions, we could use the principle that surface area scales with the square of the linear dimensions to compare the two.
Explanation:
To complete the statement about the surface areas of Figure 1 (a square pyramid) and Figure 2 (a right triangular prism), we need to consider how areas scale with the dimensions of the shapes. Salviati's example illustrates that surface areas scale with the square of the linear dimensions, which is an important concept in geometry. Applying this concept to two triangles where one is larger than the other with linear dimensions twice as long, the larger triangle will have an area four times greater (area scales with the square of the linear dimensions).
Correct solution #1: Since the larger triangle's sides are twice as long, its area is 22 = 4 times more than the smaller triangle. If we applied similar reasoning and knew the dimensions of Figure 1 and Figure 2, we could compare their surface areas. However, with the provided information, we cannot definitively complete the given statement about the surface area of the pyramid relative to the prism without the specific measurements of each figure.
By understanding that the surface area of shapes scales with the square of their dimensions and using examples like cutting the larger triangle into four smaller ones (correct solution #2), we can tackle the surface area comparison confidently, provided we have the necessary dimensions.
One pallet can store 15^5 water bottles. A stock room receives 15^13 water bottles.
Enter the number of pallets needed to store all the water bottles the stock room received.
___pallets
Answer:
3 pallets
Step-by-step explanation:
Divide to find the amount of pallets:
Subtract Exponents to divide
15^13 / 15^5 = 13 - 5 = 8 - 5 = 4 (subtracted 2 times)
You need three to store ALL the water
The stock room will need [tex]15^8[/tex] pallets to store the received [tex]15^13[/tex] water bottles since each pallet can store [tex]15^5[/tex] water bottles and we divide the total number by the pallet capacity.
To calculate the number of pallets needed to store all the water bottles the stock room received, we need to divide the total number of water bottles by the number of bottles a single pallet can hold.
The pallet can store 155 water bottles, and the stock room receives 1513 water bottles. By dividing the total number of bottles by the capacity of a pallet, the calculation is:
1513 ÷ 155 = 1513-5 = 158
Therefore, the stock room will need 158 pallets to store all the received water bottles.
ASAP
How to do
With steps
Thx
Answer:
Angle A measures 180° - (24° + 55°) = 180° - 79° = 101°.
Angle x measures 360° - 101° = 259°.
what is 7pounds equal to in ounces
Answer: that would be 112 oz
Step-by-step explanation:
Answer:
I believe the correct answer is 112 Ounces
Step-by-step explanation:
: 16 (1 lb = 16 oz)
which means you would do 7 times 16
Lance is 5 feet tall. His shadow is 8 feet long. At the same time of day trees shadow is 32 feet long. What is the height of the tree in feet.
Set u a ratio of height over shadow:
Lance = 5 feet tall / 8 foot shadow
Tree = X feet tall / 32 foot shadow.
Set the ratios equal to each other and solve for X:
5/8 = x/32
Cross multiply:
8x = 160
Divide both sides by 8:
x = 160/8
x = 20
The tree is 20 feet tall.
When you divide a unit fraction by a whole number number, will the quotient be greater than or less than the unit fraction?
Answer:
it will be less than
Step-by-step explanation:
Answer:less than
Step-by-step explanation:
Jeremy says that if you translate, rotate, or reflect a polygon, the area of the image is the same as the area of the original figure. Do you agree or disagree? Explain your choice.
Answer:
yes
Step-by-step explanation:
as long as the polygon is not dilated or the size of the polygon is not changed in any way, the area should stay the same.
Which expression is equivalent to 2(2a-5) - (a-3)?
A-2
3a-7
A-7
3a-13
Answer:
3a - 13
Step-by-step explanation:
2(2a - 5) - (a - 3)
4a - 10 - a - 3
Combine like terms:
4a - a - 10 - 3
3a - 13
Answer:
3a-13
Step-by-step explanation:
Which set of points represents a function?
A. (7, 1), (1, 2), (5, 3), (7, 3), (6, 3)
B. (1, 7), (6, 1), (7, 3), (4, 9), (6, 3)
C. (2, 1), (2, 4), (5, 3), (4, 9), (6, 3)
D. (1, 7), (2, 1), (5, 3), (4, 9), (6, 3)
Answer:
D
Step-by-step explanation:
D would be the correct answer because the x values have their individual y values. D is the only answer where the x point doesn't repeat, and the only time it can repeat is if the x points have the same y value such as: (2,4) (2,4)
For each value of x, the value of y is different. Then the correct option is D.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
Individual y values exist for each of the x values. The only instance the x point can recur is if the x locations have about the same y value, as in D. (2,4).
Then the points represents a function is (1, 7), (2, 1), (5, 3), (4, 9), (6, 3).
Thus, the correct option is D.
More about the function link is given below.
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cual es la raiz cuadrada de 81
La raíz de la cuadra de 81 es 9
Answer:
the square root o 81 is 9
Step-by-step explanation:
9x9=81
On May 9, 2014 Jason made a deposit of $650.00. What is his balance after this transaction?
A) $540.28
B) $832.45
C) $1190.28
D) $1548.11
Answer:
What did he have before?
Step-by-step explanation:
A is the correct answer
mountain bike tire completes 20 revolutions and travels 136 feet. Rounded to the nearest inch, what is the diameter of the bike’s tire?
Answer: 26in
s=r*theta
r=s/theta
d=r*2
136ft=r*40pi
r=136/40pi=1.082ft
d=1.082*2=2.1645ft*(12in/1ft)=25.97in
Rounded to nearest in is 26in diameter
The diameter of the bike's tire is calculated by dividing the total distance traveled by the number of revolutions to find the circumference and then dividing the circumference by pi (π) to find the diameter, which is approximately 26 inches.
Explanation:To find the diameter of the bike’s tire, given that it completes 20 revolutions and travels 136 feet, we can use the relationship between the circumference of a circle (in this case, the tire) and its diameter.
First, we calculate the circumference of the tire by dividing the total distance traveled by the number of revolutions:
Circumference = Total Distance ÷ Number of Revolutions
Total Distance = 136 feet (1 foot = 12 inches, so convert feet to inches for precision)
Total Distance in inches = 136 feet × 12 inches/foot = 1632 inches
Circumference = 1632 inches ÷ 20 = 81.6 inches
Now, we use the circumference to find the diameter:
Circumference = π × Diameter
Diameter = Circumference ÷ π
Diameter ≈ 81.6 inches ÷ π ≈ 26 inches
Therefore, the diameter of the bike’s tire, rounded to the nearest inch, is approximately 26 inches.
You save 3 ,260.00 in a savings account earning a 3.55% APR compounded monthly. How much is the total interest earned by the end of the third month?
The answer will be $29.02. :)
Answer:
$29.02.
Step-by-step explanation:
We have been given that you save 3 ,260.00 in a savings account earning a 3.55% APR compounded monthly. We are asked to find the total interest earned by the end of the third month.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Amount of interest after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of periods interest is compounded per year,
t = Time in years.
[tex]3.55\%=\frac{3.55}{100}=0.0355[/tex]
[tex]\text{3 months}=\frac{3}{12}\text{ year}=\frac{1}{4}\text{ year}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]A=3,260(1+\frac{0.0355}{12})^{12\times \frac{1}{4}}[/tex]
[tex]A=3,260(1+0.002958333)^{3}[/tex]
[tex]A=3,260(1.002958333)^{3}[/tex]
[tex]A=3,260*1.00890128109888[/tex]
[tex]A=3289.0181763823\approx 3289.02[/tex]
Now, we will subtract principal amount from final amount to find amount of interest.
[tex]\text{Amount of interest}=3289.02-3260[/tex]
[tex]\text{Amount of interest}=29.02[/tex]
Therefore, you will earn am amount of $29.02 by the end of the third month.
5 college students were asked how many hours of sleep did they get at night on the average the responses were a 7 hours 9 hours 5 hours 6 hours and 8 hours what is the average amount of hours of sleep do college students got in a night
7 Hours on Average
add up all the hours and you get 35
then divide 35 by the number of given hours which is 5
35/5 = 7
so the average amount of hours slept was 7
Answer:
7 hours
Step-by-step explanation:
To find this average, add up the five data points given and divide your result by five (5):
(7 + 9 + 5 + 6 + 8) / 5 = 35 / 5 = 7
This group of students averaged 7 hours of sleep per night.
Julia bought 300 pounds of grain for her
horses. When a rainstorm flooded the
storage shed, 30% of the grain rotted and
had to be thrown out. How many pounds
of grain will Julia be able to use?
Answer: 210
Step-by-step explanation:
10% of 300 is 30
30x3=90
30%=90
90-300=210
Answer:
210 pounds
Step-by-step explanation:
So you can solve this by making an equation of 300 times 30 is equal to 100 times x so 9000 is equal to 100x so x=90. So she can use 210 pounds.
Chuck can afford a $490-per-month car payment, and he's interested in either
a convertible, which costs $28,700, or a sports car, which costs $29,200. If he
is being offered a 6-year car loan with an APR of 6%, compounded monthly,
which car can Chuck afford?
Answer:
Chuck can afford both the convertible and sports car APEX
Step-by-step explanation:
Answer:
We can say that Chuck can afford both the cars.
Step-by-step explanation:
The EMI formula is :
[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
Case 1:p = 28700
r = 6/12/100=0.005
n = 6*12=72
Putting the values in the above formula, we get:
[tex]\frac{28700*0.005*(1.005)^{72} }{(1.005)^{72}-1 }[/tex]
Monthly payment is = $475.67
Case 2:p = 29200
r = 6/12/100=0.005
n = 6*12=72
Putting the values in the above formula, we get:
[tex]\frac{29200*0.005*(1.005)^{72} }{(1.005)^{72}-1 }[/tex]
Monthly payment is = $483.96
We can see that in both the cases, the monthly payments or EMI's are less than $490.
Therefore, we can say that Chuck can afford both the cars.
In 2012, the population of a city was 5.57 million. The exponential growth rate was 3.69% per year.
A) find the exponential growth function.
B) Estimate the population of the city in 2018.
C) When will the population of the city be 8 million?
D) Find the doubling time.
Answer:
c
Step-by-step explanation:
Find the measure of CD.
Round to the nearest tenth.
PLEASE NEED HELP!!!
Answer:
89.0°
Step-by-step explanation:
The measure of arc CD is the same degree measure as the central angle.
To find the central angle use the right triangle.
The segment from the centre to the chord is a perpendicular bisector, thus
the third side of the triangle = 12.7 ÷ 2 = 6.35
Calculate one half of the central angle using the sine ratio and multiply by 2 for the whole central angle
sin( one- half ) =[tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6.35}{9.06}[/tex], hence
central angle = 2 × [tex]sin^{-1}[/tex] ([tex]\frac{6.35}{9.06}[/tex] ) ≈ 89.0°
Hence measure of CD ≈ 89.0°
What do z€ R mean for math as an answer to a inequality
Answer:
Its used for the domain and it means "the members of all REAL numbers" which refers to their being no imaginary number, for instance in inequalities that have square roots, it cant be a negative number otherwise you will get a imaginary number.
Step-by-step explanation:
The 'z€ R' notation means 'z is an element of R' or 'z belongs to R', which signifies that the variable z is a part of the set of real numbers. This indicates the domain for the variable in an inequality. Also, the principle of the z-score in statistics describes how many standard deviations above or below the mean a certain value lies.
Explanation:The notation z€ R in mathematical terms is used to indicate that the variable z belongs to the set of real numbers. Real numbers (often denoted by R) include all the numbers that can be shown on the number line; this set comprises rational (e.g., integers, fractions) and irrational numbers (like roots of numbers that are not perfect squares). When related to an inequality, this statement provides a domain of numbers that can satisfy said inequality, helping solve problems or equations.
A related concept is the z-score in statistics. The z-score tells you how many standard deviations a value is above or below the mean. Values larger than the mean have positive z-scores, but smaller values have z-scores that are negative. The absolute value of the z-score indicates the distance from the mean, irrespective of direction.
An example: a variable x in an equation can be represented in terms of z-score as x₁ = µ + zơ, which would mean that x is greater than the mean µ when z is positive, and less when z is negative.
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A right rectangular prism's edge lengths are 7 1/ 4 inches, 8 inches, and 9 inches. How many unit cubes with edge lengths of 1 2 inch can fit inside the prism? A) 224 unit cubes B) 940 unit cubes C) 1360 unit cubes D) 4176 unit cubes
Answer:
D) 4176 unit cubes
Step-by-step explanation:
Length of the right rectangular prism [tex]=7\frac{1}{4}[/tex] inches
Width of the right rectangular prism [tex]=8[/tex] inches
Height of the right rectangular prism [tex]=9[/tex] inches
Then volume of the right rectangular prism = (Length)(Width)(Height)
[tex]=\left(7\frac{1}{4}\right)\left(8\right)\left(9\right)[/tex]
[tex]=\left(7.25\right)\left(8\right)\left(9\right)[/tex]
[tex]=522[/tex] cubic inches
Now volume of the small cubic prism [tex]=(Length)^3=\left(\frac{1}{2}\right)^3=\frac{1}{8}[/tex]
Then number of cubes that can fit into the right rectangular prism [tex]=\frac{522}{\left(\frac{1}{8}\right)}=522*8=4176[/tex]
Hence correct choice is D) 4176 unit cubes