First represent your 6 consecutive integers as follows.
X ⇒ first integer
X + 1 ⇒ second integer
X + 2 ⇒ third integer
X + 3 ⇒ fourth integer
X + 4 ⇒ fifth integer
X + 5 ⇒ sixth integer
Since their sum is 597, our equation reads
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 597.
Simplifying on the left we get 6x + 15 = 597.
Now subtract 15 from both sides to get 6x = 582.
Now dividing both sides by 6, we find that x = 97.
So our first integer, x, is 97.
Our third integer would be x + 2 or 97 + 2 which is 99.
Horace takes a taxi uptown, and the fare is $12.78. He wants to give the driver a 10% tip.
If Horace gives the driver a $20 bill, how much change should he ask for?
Answer:
$5.94
Step-by-step explanation:
12.78 + 10% (1.28) = 14.06
20.00 - 14.06 = 5.94
I will mark brainliest if you are correct!
When solving the equation, which is the best first step to begin to simplify the equation?
-2 (x + 3) = -10
A. (-2) (-2) (x + 3) = -10 (-2)
B. -1/2 (-2) (x + 3) = -10 (-1/2)
C. -2/2 (x + 3) = -10/2
-2/-10 (x + 3) = -10/-10
Answer:
i think the answer is C
Step-by-step explanation:
Answer:
Look below.
Step-by-step explanation:
Uh here's what I did:
-2x-6= -10
Add 6 to both sides.
-2x=-4
Divide both sides by -2
x=2
Derek is planning on covering an entire drum in leather. The diameter of the drum is 10 inches, and the height of the drum is 16 inches. What is the minimum amount of leather that Derek will need to cover the drum?
Answer: 694.4 in^2
Step-by-step explanation:
We have a cylinder with:
diameter = d = 10 inches
heigth = h = 16 inches.
The total surface of a cylinder is equal to:
S = h*2*pi*(d/2) + 2*pi*(d/2)^2
we can replace the numbers and get:
S = 16*2*3.14*(10/2) + 2*3.14*(10/2)^2 = 659.4 inches squared
Regina bought a book for $12 and a game for $14 she paid $40 how much change should Regina receive
Answer:Regina recieved $14 dollars of change
Step-by-step explanation:
12+14=26
40-26=14
The change received by Regina is $14.
What is a word problem?
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Regina bought a book for price = $12
Regina bought a game for price = $14
Total amount paid by Regina = $40
The Regina should receive the change,
⇒ [tex]Change = 40-(12+14)[/tex]
⇒ [tex]Change = 40-26[/tex]
⇒ [tex]Change = 14[/tex]
Hence we can conclude that the change received by Regina is $14.
Learn more about word problems here
brainly.com/question/20594903
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Determine the volume of the cylinder
Answer:
about 904.78
Step-by-step explanation:
πr^2h pi(6)^2 * 8
Tien has six coins in her pocket. She has at
least one quarter, one dime, one nickel, and
one penny. Use an organized list to show
how many different ways Tien might have
more than 60¢.
Answer:
10 dimes
Step-by-step explanation: 10 cents x 6 = 60 cents
Simplify the expression
13 (9x)
13(9x)
13 * 9x = 117x
Answer:
[tex]117x[/tex]
Step-by-step explanation:
[tex]13(9x) \\ = 117x[/tex]
A factory sells backpacks for $40.00 each. The cost to make 1 backpack is $10.00. In addition to the cost of making backpacks, the factory has operating expenses of $12,000 per week. The factory’s goal is to make a profit of at least $9,800 per week. Which inequality represents the number of backpacks, x, that need to be sold each week for the factory to meet this goal?
Answer:
300 Backpacks each week]
Step-by-step explanation:
dont have an explanation srry but the answer is totally 300 backpacks a week
Answer:
30
Step-by-step explanation:
On Earth you weigh 54.5 kilograms, while on the moon you weigh 9,071 grams. How many more grams do you weigh on Earth than on the moon?
BALLOON The angle of depression from a hot air balloon in the air to a person on the ground is 41°. If the person steps back 12 feet, the new angle of depression is 25°. If the person is 6 feet tall, how far off the ground is the hot air balloon?
Answer:
16.06 ft
Step-by-step explanation:
The figure is attached below.
In triangle ACB:
[tex]tan(41)=\frac{x}{y} \\x=ytan(41)[/tex]
In triangle ADB:
[tex]tan(25)=\frac{x}{y+10} \\(y+10)tan(41)=x[/tex]
Therefore equating both equations gives:
[tex]ytan(41) = (y+10)tan(25)\\ytan(41) = ytan(25)+10tan(25)\\ytan(41)-ytan(25)=10tan(25)\\y(tan(41)-tan(25))=10tan(25)\\y=\frac{10tan(25)}{(tan(41)-tan(25)} =11.5715ft[/tex]
Therefore x = 11.5715*tan(41) = 10.06 ft
The distance of the jot air balloon to ground = 10.06 + 6 = 16.06 ft
Factor the perfect square trinomial 25x^2-60x+36
Since it is a perfect square trinomial, it is of the form:
a^2x^2-2abx+b^2 which simplifies to (ax-b)^2
Therefore:
sqrt(a)=sqrt(25)=5
sqrt(b)=sqrt(36)=6
Plug in a and b:
(ax-b)^2
(5x-6)^2
Test to make sure it did fit the formula:
-2abx=-60 (where x is 1)
-2(5)(6)=-60
-2(30)=-60
-60=-60
Answer:
(5x-6)^2
the circumference of a circle is 16tt inches what is the radius of the circle
what is the distance between (2,6) and (5,10)?
Distance formula: d = √(x2-x1)^2 + (y2-y1)^2
d = √(5-2)^2 + (10-6)^2
d = √3^2 + 4^2
d = √9 + 16
d = √25
d = 5
The distance is 5 units.
Best of Luck!
what is the area and perimeter of a rectangle that has base of 18 inches and height of 5 inches
Answer:
area is 90 and perimeter is 46
Step-by-step explanation:
the area for a rectangle is l * w, so 18*5 is 90, and the perimeter is 2l+2w, which is 46.
Answer:
Area 90
perimeter 46
Step-by-step explanation:
To find area, you multiply both sides.
to find perimeter, you add up all the sides. Make sure to double each number.
A triangle has the angle measurements of 62 degrees and 91 degrees. What is the measurement of the third angle?
a
b
29 degrees
153 degrees
27 degrees
180 degrees
С
d
Answer:
27
Step-by-step explanation:
180 is always the total of the triangle measurements. Therefore,
180-(91+62)=27
Answer:
27°
Step-by-step explanation:
A triangle is 180 degrees
So you begin with what you know 91 degrees and 62degrees
So 180-91-62=27degrees
So your answer is 27degrees
A sphere-shaped beach ball is 16 inches in diameter. How many cubic inches of air will the ball hold when it is fully inflated? Use 3.14 for π. Round your answer to the nearest tenth.
a.682.7 cubic inches
b.2,143.6 cubic inches
c.5,461.3 cubic inches
d.17,148.6 cubic inches
Factor the polynomial expression 16y4 - 256x12.
Answer:
[tex]16y^{4} -256x^{12} =16(y^{4} -16x^{12})\\ 16[(y^{2})^{2}-(4x^{6})^{2} ]\\ =16(y^{2} -4x^{6})(y^{2} +4x^{6}) \\\\=16(y^{2} -(2x^{3})^{2}) (y^{2} +4x^{6}) \\=16(y-2x^{3})(y+2x^{3}) (y^{2} +4x^{6}) \\[/tex]
Step-by-step explanation:
Answer:
16y4 - 625x4 = (4y2 + 25x2)(2y + 5x)(2y-5x)
Step-by-step explanation:
dis right
Which set of angles can form a triangle?
A: 2 acute and 1 right
B: 1 acute and 2 obtuse
C: 1 acute and 2 right
D: 1 acute, 1 right and 1 obtuse
Answer:
A: 2 acute and 1 right
Step-by-step explanation:
A triangle is a polygon that has 3 sides as well as three angles
Triangles can be can be classified based on their three sides as well as their three angles.
Based on their sides, we have 3 types of triangles.
1. Equilateral triangle: This means they have 3 equal sides.
2. Isoceles triangle: They have only 2 equal sides.
3. Scalene triangle: The 3 sides are not equal
Based on their angles, we have 3 triangles.
a. Acute triangle
b. Obtuse triangle
c. Right angle triangle.
One of the way by which we can form a triangle, is by forming it with 2 acute angles and 1 right angle.
Answer:
The correct option is;
A: 2 acute and 1 right
Step-by-step explanation:
Here we have the definitions of the angles as follows;
The sum of angles in a triangle = 180°
An acute angle is an angle less than 90°
An obtuse angle is an angle more 90 ° but less 180°
A right angle triangle is an angle equal to 90°
∴ A right angle triangle is an angle = 90°
Therefore, we compare each of the options
A: 2 acute and 1 right = <90 +<90 +90 < 180 =180 or >180 Possible
B: 1 acute and 2 obtuse = 1<90 + > 90 +>90 > 180°
C: 1 acute and 2 right = <90 + 90 + 90 > 180
D: 1 acute + 1 right + 1 obtuse = <90 + 90 + >90 > 180
Therefore, the only possible correct option is A.
Garry is studying a square pyramid and wants to draw a net of the figure
to help determine its surface area. Which net represents a square pyramid?
Answer:
On this picture, it is b, but for edge, it is c
Step-by-step explanation:
Answer:
c but b in the pic
Step-by-step explanation:
Determine the projection of w onto v. U=9i-6j, v= -3i-2j, w=19i+15j
Answer:
w·v = -87
Step-by-step explanation:
The projection of a vector on another vector is given by the dot product between the vectors.
Thus, you calculate the dot product between w and v:
[tex]\vec{w}=(19,15)\\\\\vec{v}=(-3,-2)\\\\\vec{w}\cdot \vec{v}=(19,15)\cdot (-3,-2)\\\\\vec{w}\cdot \vec{v}=-57-30=-87[/tex]
So, the projection of w on v is -87
Lana's little sister needs to take a bubble bath. The package says to put in a drop of bubble bath for every half gallon of water in the bath tub. Lana doesn't know how many half gallons there are, but she knows that their bathtub can hold 12 gallons of water. How many drops can she put into the bath for her sister?
Answer:
Lana can put 24 drops of bubble bath for her sister
Step-by-step explanation:
If package says to put in a drop of bubble bath for every half gallon of water in the bath tub.
If the bathtub can hold 12 gallons of water
There are 12÷1/2 gallon
=12×2/1
=24
It means there are 24 half gallons in the bathtub
If every half gallon of water requires a drop of the bubble bath
Then,
24 half gallons of water requires 24 drops of the bubble bath
Taylor has a box that contains 3 pennies, 5 nickels, and 2 quarters. If she chooses a coin out of the box without looking, and then without replacing it draws a second coin, what is the probability that both coins will be quarters?
Answer:
1/45
Step-by-step explanation:
There is 10 total coins and only 2 are quarters so that's 2/10 but one is taken out so now its 1/9 because we think its a quarter. Multiply 2/10 x 1/9 and you get 2/90 simplify it and you get 1/45
Donna took twice as long to drive 720 miles and Maple took to drive 200 miles. Find the rates and ties of both if Donna's speed exceeded that of Maple by 40 miles per hour
Answer:
Donna traveled for 8 hours at 90 mph
Maple traveled for 4 hours at 50 mph
Step-by-step explanation:
The velocity at which each person traveled is given by the distance traveled divided by the time spent (t). From the information given, the following expressions can be written
[tex]t_d = 2t_m\\V_d = V_m+40\\V_d = \frac{720}{t_d}\\V_m = \frac{200}{t_m}\\\\V_d = \frac{360}{t_m}\\ \frac{360}{t_m}=\frac{200}{t_m}+40\\t_m = 4\ hours\\t_d=2*4 = 8\ hours\\\\V_d = \frac{720}{8}=90\ mph\\V_m = \frac{200}{4}=50\ mph\\[/tex]
Therefore, Donna traveled for 8 hours at 90 mph and Maple traveled for 4 hours at 50 mph.
Emily is training for a 10K race. On day one, she runs for 20 minutes. On day two, she runs for 30 minutes. On day three, she runs for 40 minutes. If this pattern continues, how many minutes will she run on day 12?
Answer:
130
Step-by-step explanation:
:0
Jeremy’s dad is making cupcakes for his birthday. He needs 50 cupcakes in all. So far he made 13 chocolate cupcakes and 15 vanilla cupcakes. How many more cupcakes must he make?
Answer:
22 cupcakes
Step-by-step explanation:
13+15=28
50-28=22
Answer:
22 cupcakes
Step-by-step explanation:
First, let's find how many cupcakes he has already made.
He made 13 chocolate and 15 vanilla. If we add them together, we can find how many he has made total.
13+15=28
So far, he has 28 cupcakes.
He needs 50 cupcakes, and he has already made 28. The difference of the two numbers will be how many he must still make.
Subtract 28 from 50
50-28=22
So, he still has to make 22 cupcakes
Mark recently took a road trip across the country. The number of miles he drove each day was normally distributed with a mean of 450. If he drove 431.8 miles on the last day with a z-score of -0.7, what is the standard deviation?
Answer:
The (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.
Step-by-step explanation:
We can solve this question using the concept of z-score or standardized value, which is given by the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
[tex] \\ z[/tex] is the z-score.
[tex] \\ x[/tex] is the raw score.
[tex] \\ \mu[/tex] is the population's mean.
[tex] \\ \sigma[/tex] is the population standard deviation.
Analyzing the question, we have the following data to solve this question:
The random variable number of miles driven by day is normally distributed.The population's mean is [tex] \\ \mu = 450[/tex] miles.The raw score, that is, the value we want to standardize, is [tex] \\ x = 431.8[/tex] miles.The z-score is [tex] \\ z = -0.7[/tex]. It tells us that the raw value (or raw score) is below the population mean because it is negative. It also tells us that this value is 0.7 standard deviations units (below) from [tex] \\ \mu[/tex].Therefore, using all this information, we can determine the (population) standard deviation using formula [1].
Then, substituting each value in this formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
Solving it for [tex] \\ \sigma[/tex]
Multiplying each side of the formula by [tex] \\ \sigma[/tex]
[tex] \\ \sigma*z = (x - \mu) * \frac{\sigma}{\sigma}[/tex]
[tex] \\ \sigma*z = (x - \mu) * 1[/tex]
[tex] \\ \sigma*z = x - \mu[/tex]
Multiplying each side of the formula by [tex] \\ \frac{1}{z}[/tex]
[tex] \\ \frac{1}{z}*\sigma*z = \frac{1}{z}*(x - \mu)[/tex]
[tex] \\ \frac{z}{z}*\sigma = \frac{x - \mu}{z}[/tex]
[tex] \\ 1*\sigma = \frac{x - \mu}{z}[/tex]
[tex] \\ \sigma = \frac{x - \mu}{z}[/tex]
Then, this formula, solved for [tex] \\ \sigma[/tex], will permit us to find the value for the population standard deviation asked in the question.
[tex] \\ \sigma = \frac{431.8 - 450}{-0.7}[/tex]
[tex] \\ \sigma = \frac{-18.2}{-0.7}[/tex]
[tex] \\ \sigma = 26[/tex]
Thus, the (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.
What is the simplified form of - picture
Answer:
the answer and explanation are In the picture
hope this helps
please like and Mark as brainliest
PLEASE HELP image below
Answer: 73
Step-by-step explanation:
[tex]7d^2+10\\d=3[/tex]
[tex]7(3)^2+10\\7(9)+10\\63+10\\73[/tex]
Answer:
73
Step-by-step explanation:
d =3
-> 7 * [tex]3^{2}[/tex] + 10 = 7*9 +10 = 63+10 = 73
What is the radius and diameter of the following circle?
111 cm
Radius
cm
Diameter =
cm
Answer:
Diameter = 212 cm
Step-by-step explanation:
D= 2r
What happens to the parabola when a<1 compared to the parent function?
Answer: The parabola is wider than the parent function
Step-by-step explanation:
If "a" is a fraction less than one, then the parabola becomes wider.
See graph (attached)
