Correct Question
30th term of AP 10, 7, 4 is
Answer:
The 30th term is -77
Step-by-step explanation:
Required
Determine the 30th term of the given progression
First, we need to determine the common difference (d);
[tex]d = T_2 - T_1[/tex]
[tex]d = 7 - 10[/tex]
[tex]d = -3[/tex]
The nth term of an AP is calculated by
[tex]T_n = a+ (n -1) d[/tex]
In this case;
n = 30;
a = First term = 10
d = -2
Substitute these values in the given formula
[tex]T_{30} = 10+ (30 -1) * -3[/tex]
[tex]T_{30} = 10+ (29) * -3[/tex]
Open the bracket
[tex]T_{30} = 10-87[/tex]
[tex]T_{30} = -77[/tex]
Hence, the 30th term is -77
A full case of soda contains 24 bottles. Tom filled a partially empty case by putting in seven bottles. How many bottles were in the case before he filled it?
Answer:
17 bottles
Step-by-step explanation:
full case: 24
he added 7 bottles to fill a case
24-7=17
Which of the following is a rational number?
square root of 22, square root of 23, square root of 24, square root of 25
square root of 22
square root of 23
square root of 24
square root of 25
Answer:
square root of 25 because it equals 5
Step-by-step explanation:
Because the square root of the other they don’t replete or terminate.
square root of 22 is 4.6904157...
square root of 23 is 4.7958315...
square root of 24 is 4.8989794...
square root of 25 is 5
Convert the angle 4.5 radians to degrees, rounding to the nearest 10th
Answer:
257.8
Step-by-step explanation:
The angle of 4.5 radians is approximately equal to 257.8 degrees.
How to convert radians to degrees?The formula to convert radians to degrees is written as follows:
degrees = radians x (180/π)
where π (pi) is approximately 3.14159.
To convert 4.5 radians to degrees, we can use the conversion factor 180/π, which is the number of degrees in one radian.
degrees = 4.5 x (180/π)
degrees ≈ 257.87 degrees (rounded to the nearest 10th).
Therefore, the angle of 4.5 radians is approximately equal to 257.8 degrees.
Learn about the conversion of radians to degrees here:
https://brainly.com/question/31673497
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Micheal recorded the number of points his team scored for the first seven basketball games, 64,58,60,52,56,62,54 Which box plot correctly represents the data?
Answer:
The correct box plot is B (Bottom left)
Step-by-step explanation:
I have attached the appropriate picture containing the box plots to this answer. In order to choose the most appropriate box plot, we have to find the median of the distribution and locate the box plot showing the correct median. This is done as follows:
To find the median, we will first arrange the distribution in ascending (or descending) order
Median = 52, 54, 56, 58, 60, 62, 64
Next, we will group the data into two halves, and choose the middle term, which is 58. this becomes the median.
From the diagram, box plots, A, B and C have their median as 58, in order to determine the correct plot, we will find the medians to the lower and upper halves of the distribution. This is done as follows:
Lower half: 52, 54, 56, 58
Median of lower half = (54 + 56) ÷ 2 = 55
upper half = 58, 60, 62, 64
Median of upper half = (60 + 62) ÷ 2 = 61
From the picture the plot with these three medians from lower half to upper half (55, 58, 61) is plot B (bottom left)
Note the medians are the lines that form the boundaries and at the middle of the box.
Answer:
The answer is B bottom left :
If m_ABD
-
83° and m ABC = (x + 10) and mZDBC
(2 + 10) and mZDBC = (4x – 12), what is the measure of each angle?
B
Enter the correct numbers in the boxes.
lo
mABC -
mZDBC =
Answer:
m<ABC=27°
m<DBC=56°
Step-by-step explanation:
(x+10)+(4x-12)=83
5x-2=83
5x=83+2
5x=85
x=17
m<ABC=(x+10)=(17+10)=27°
m<DBC=(4x-12)=(4*17-12)=56°
I NEED HELP, I'VE BEEN STUCK ON THIS...Find the volume of this triangular prism. Enter only the numerical part of your answer in square units.
Answer:
[see below]
Step-by-step explanation:
Volume of a triangular prism is: [tex]V=\frac{1}{2}bhl[/tex]
We are given the base of 5, the length of 12, and the height of 8. All measurements are in meters.
[tex]V=\frac{1}{2}(5*12*8)\\\\V=\frac{1}{2}(480)\\\\V=240[/tex]
The volume of the prism should be 240 square meters.
Answer:
V = 240 m^3
Step-by-step explanation:
The volume of a triangular prism is
V = Bh where B is the area of the base and h is the height
B = the area of the triangular base
B = 1/2 bh
B = 1/2 *5*12
B = 30 m^2
The volume is
V = 30 * 8
V = 240 m^3
Ms. Malle owns a restaurant. Typically 3/20 of the customer’s order fish, while 7/20 of the customer’s order poultry. What fraction of her customers order either fish or poultry?
Please help me with this question ASAP.
How many planes of symmetry are there in a regular hexagonal prism?
Answer:
we have 6 planes of symmetry
please help :) Which sentence is true? A. 9.46 times 10 to the 12 power > 4.0 times 10 to the 13 power B. 9.46 times 10 to the 12 power < 4.0 times 10 to the 13 power
Answer:
B
Step-by-step explanation:
The problem is simple because they use powers of 10. When something is multiplied by a power of ten, it is essentially moving the decimal point over for every power.
9.46x10^12= 9460000000000
4.0x10^13= 40000000000000
Although 4 itself is less than 9.46, since is is being multiplied by 10^13, it will be one decimal place bigger.
10 People fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is 5 feet deep on both sides of the street along a 2-mile section of a parade route.
Answer:
The size of the crowd that is 5 feet deep on both sides of the street along a 2-mile section of a parade route is 42,240 people
Step-by-step explanation:
The number of people that can fit comfortably in a 5 feet by 5 feet area = 10
Therefore;
The ratio of the number of people per unit area = 10/(5 × 5) = 10/25
The area, A, occupied by the crowd = 5 feet × 2 mile × 2
2 miles = 10,560 feet
∴ A = 5 feet × 10,560 feet × 2 = 105,600 ft²
We then have;
[tex]\dfrac{Number \ of \ people}{105,600} =\dfrac{10}{25}[/tex]
[tex]Number \ of \ people = {105,600} \times \dfrac{10}{25} = 42,240 \ people[/tex]
change to a whole number or mixed number 12/7
Answer:
1 5/7
Step-by-step explanation:
[tex]\frac{12}{7} \\= 12\div 7 = 1\: remainder\: 5\\\\= 1 \frac{5}{7}[/tex]
Answer: 1 and 5/7
Step-by-step explanation: To write an improper fraction as a mixed number,
divide the denominator into the numerator.
So here, we have 7 divided into 12.
7 divides into 12 one time, 1 × 7 is 7, and 12 - 7 is 5.
So 7 divides into 12 one time with a remainder of 5.
So we have 1 whole and 5 out of 7 parts or 1 and 5/7.
So the improper fraction 12/7 can be written
as the mixed number 1 and 5/7.
Plz help me ! In triangle ABC, angle A = 90° and angle B = 25°. In triangle DEF, angle E =
25° and angle F = 65°. Are the Triangles similar?
An account pays 8% per year simple interest paid a new one, the amount in the account is $850. How much is the account in year 6?
Answer:
1258
Step-by-step explanation:
SI = (P x R x T) / 100
SI = Simple Interest
P = Principal
R = Rate
T = Time
SI = (850 x 8 x 6)/100
=> SI = 85 x 8 x 6 /10
=> SI = 680 x 6 /10
=> SI = 68 x 6
=> SI = 408
The total amount after 6 years = Principal + Simple Interest
=> Total Amount = 850 + 408
=> Total Amount = 1258
After 6 years, the amount in account is 1258.
You buy six T-bone steaks that cost $15.99 per pound. The weight that is listed on the package is 5.77 pounds. The scale that weighed the package is accurate to within 1 32 pound. How much per kilogram might you be undercharged or overcharged? (Round to the nearest cent.)
Answer:
Amount per kilogram, undercharged or overcharged is 0.50
Step-by-step explanation:
Given:
cost of T-bone steaks per pound = $ 15.99
weight listed on package = 5.77 lb
Accuracy of the scale = 1/32 lb
To find:
Amount undercharged or overcharged
Solution:
Let x represent the weight of the package.
Then compute the error in the weight
| x - 5.77 | < 1 / 32
This makes an absolute value inequality
If an inequality is given in the form | x | < a then solution is in the form:
–a < x < a.
If an inequality is in the form | x | > a, then solution splits in the form:
x < –a or x > a.
compute the amount undercharged or overcharged:
First multiply the above inequality by cost of T-bone steaks per pound
15.99 |x - 5.77| < 15.99 (1 / 32)
15.99 |x - 5.77| < 15.99(0.03125)
15.99 |x - 5.77| < 0.4996875
15.99 |x - 5.77| < 0.50
Hence the amount undercharged or overcharged is $0.50
u need help ASP .
f(x)=1-3X and g (x)=x+4 calculate gf(-2)
Answer:
gf (-2) = 11
Step-by-step explanation:
[tex]f(x) = 1 - 3x \\ g(x) = x + 4 \\ gf( - 2) = ..[/tex]
[tex]gf = .. \\ g(1 - 3x) \\ = 1 - 3x + 4 \\ = - 3x + 5 \\ gf = - 3x + 5[/tex]
[tex]gf( - 2) = - 3( - 2) + 5 \\ = 6 + 5 = 11[/tex]
The length of a rectangle is 3cm longer than its width.If the perimeter of the rectangle is 54cm,find its length in cm.
Answer:
length = 15 cm
Width = 12 cm
Step-by-step explanation:
Let width = w cm
Length = w + 3
Perimeter of rectangle = 54 cm
2 * (length + width) = 54
2 * (w+3 + w) = 54 {Add like terms}
2 *(2w + 3) = 54
2*2w + 2 * 3 = 54
4w + 6 = 54
Subtract 6 form both sides
4w = 54 - 6
4w = 48
Divide both sides by 4
w = 48/4
w = 12 cm
Length = 12 + 3= 15 cm
Answer:
Length = 15cm
Step-by-step explanation:
let width be x
length = x+3
Perimeter = 2(l + b)
Perimeter = 54cm
equating:
2(x + x + 3) = 54
2(2x +3) = 54
4x + 6 = 54
4x = 54 - 6
4x = 48
x = 48/4 = 12
width = x = 12cm
length = x +3 = 12 + 3 = 15cm
I'm trying to find 1, 2, & 3 but idk how? Sry if it's sideways I'm new
Answer:
Step-by-step explanation:
m∠1+∠2=180
2x+40+2y+40=180
2x+2y=180-80
2x+2y=100
x+y=50
x=50-y
m∠1=m∠3
2x+40=x+2y
2x-x=2y-40
x=2y-40
2y-40=50-y
2y+y=50+40
3y=90
y=30
x=50-y=50-30=20
m∠1=2x+40=2×20+40=80°
m∠2=2y+40=2×30+40=60+40=100°
m∠3=x+2y=20+2×30=80°
What is the equation for the axis of symmetry of a parabola?
Answer:
The graph of the parabola is represented by the quadratic function
y = a( x - p )2 + q which has an axis of symmetry represented by the equation of the vertical line x = p.
Step-by-step explanation:
Answer:
x=-b/2a
Step-by-step explanation:
Find f(−1) given that f(x)=x3+2x2+3x+4.
A. 10
B. -2
C. 2
D. -10
Answer:
The answer is option C
Step-by-step explanation:
f(x) = x³ + 2x² + 3x + 4
To find f(-1) substitute the value of x that's
- 1 into f(x)
That's
[tex]f( - 1) = ({ - 1})^{3} + 2 ({ - 1})^{2} + 3( - 1) + 4 \\ = - 1 + 2(1) - 3 + 4 \\ = - 1 + 2 - 3 + 4 \\ = 1 - 3 + 4[/tex]We have the final answer as
[tex]f( - 1) = 2[/tex]Hope this helps you
What is the area, in square meters, of the shaded part of the rectangle below?
6 m
14 m
13 m
Answer:
130 meters squared
Step-by-step explanation:
14-6=8
8*13/2=52
14*13=182
182-52=130 meters
Answer:
130 square metres
Step-by-step explanation:
The shaded area is a trapezium.
Therefore, the rule for its area is base1+base2/2xh
base1=6
base2=14
height = 13
Therefore, 6+14/2 x 13
= 130
Hope that helped!!! k
Y = A system of equations. Y equals StartFraction one-half EndFraction x minus 6. X equals negative 4.X – 6 x = –4 What is the solution to the system of equations?
Answer:
[tex]x = -4, y =-8[/tex] is the solution to the system of equations.
Step-by-step explanation:
Given the system of equations as:
[tex]y= \dfrac{1}{2}x-6[/tex]
and
[tex]x =-4[/tex]
To find:
The solution to the system of equations = ?
Solution:
Here, we are given two equations and two variables i.e. [tex]x[/tex] and [tex]y[/tex].
So, we can solve the system of equations for the values of [tex]x[/tex] and [tex]y[/tex].
Let us first consider the 2nd equation.
[tex]x =-4[/tex] we already have the value of [tex]x[/tex].
Now, let us put the value of [tex]x[/tex] in the 1st equation to find the value of [tex]y[/tex].
[tex]y= \dfrac{1}{2}x-6[/tex]
[tex]\Rightarrow y= \dfrac{1}{2}\times (-4)-6\\\Rightarrow y= -\dfrac{1}{2}\times 4-6\\\Rightarrow y= -2-6\\\Rightarrow \bold{y =-8}[/tex]
So, the solution to the system of equations is:
[tex]x = -4, y =-8[/tex]
This for math. Rewriting Fractions
How do you decide which number to use in the Giant One?
Answer:
factor of hundred is
100 - 1, 2,4,5,10,100
Whats the answer? For all of them
Answer:
cow = 4
pig = 5
chicken = 9
horse = 3
horse + chicken - pig =7
find the area of the 1/4 circle when the radius is 8
Answer:
Method 1 (using the area of a whole circle and dividing by 4)
First work out the area of the whole circle by substituting the radius of 8cm into the formula for the area of the circle:
A = π ×r²
= π ×8²
= 64π (leave the answer as an exact solution as this need to be divided by 4).
So all you need to do now is divide the answer by 4:
Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² to 3 significant figures.
Method 2 (using ¼ πr²)
Substitute r = 8 directly into the formula A = ¼ πr².
A = ¼ πr².
A = ¼ × π × 8².
A = 50.3 cm²
As you can see it gives exactly the same answer as method 1.
Answer:
64pi / 4 = 16pi, or 50.27
Step-by-step explanation:
We use the area formula:
π * r^2 = Area
Substitute in 8 for r to get 64pi
Then all you have to do is divide 64pi by 4 to find a quarter of the area of the circle, which is 16pi. Or if you want rounded to nearest tenth, 50.27
Please turn this word problem into an equation.... Braden and Michael are running laps. Braden runs 3 less than twice as many as Michael. Together they run 12 laps.
Answer: x+ 2x -3 = 12
Step-by-step explanation:
x represents Michael's laps. 2x -3 represents Braden's laps. Added together for a total of 12
One step further would be to combine the x terms, so the equation becomes 3x - 3 = 12
Nine less than the quotient of a number and 2 is 11. Find the number.
18 + ?t = 24 what number should be the coefficient of t?
Answer:
if t is 2 then coefficient will be 3
if t is 3 then coefficient will be 2
Step-by-step explanation:
18 + ?t = 24
subtracting 18 from sides
18 + ?t - 18= 24 -18 = 6
=> ?t = 6 = 2*3
as value of both ? and t is not given thus both can take value of 2 and 3
hence,
if t is 2 then coefficient will be 3
if t is 3 then coefficient will be 2
Answer:
the answer is 123
Step-by-step explanation:
0.227 convert into rational number
Answer:
[tex]\frac{227}{1000}[/tex]
Step-by-step explanation:
A rational number has the form
[tex]\frac{a}{b}[/tex] where a and b are integers
Given
0.227 ← with the 7 in the thousandths place value position, then
= [tex]\frac{227}{1000}[/tex]
Explain the Golden Rule for solving equations using an example. NEED HELP QUICK
Answer:
See explanation
Step-by-step explanation:
The golden rule for solving equations is to
A. Simplify each side of the equation by removing parentheses and combining like terms
B. Add/Subtract to isolate the term with the variable on one side
C. Use multiplication/division to isolate the variable
Let's assume we have the equation [tex]2x + 3x + (5\cdot2) = 35[/tex]
The first thing we need to do is solve inside the parentheses and combine like terms. 2x and 3x are like terms, so:
[tex]2x + 3x + 10 = 35\\\\5x + 10 = 35[/tex]
Now we have to subtract/add to isolate the term with the variable. To do this, we can subtract 10 from both sides.
[tex]5x + 10 - 10 = 35-10\\\\5x = 25[/tex]
Now we divide to isolate x.
[tex]5x \div 5 = 25\div5\\\\x = 5[/tex]
Hope this helped!
a perfect is to be chosen from a class of 16 girls and 14 boys.what is the probability that the prefect is a girl
Answer:
8/15Step-by-step explanation:
[tex]16\:girls \\14\:boys\\\\Probability = \frac{Event}{Total \:possible\:outcome}\\\\ Event=16\\\\ Total\:possible\:outcome = 16+14=30\\\\P = \frac{16}{30}\\ \\Probability = \frac{8}{15}[/tex]