Answer:
-24 - 4x + 6= 16x + 22
-29 -22 = 16x +4x
-51 = 20x
x= -51/20
Given: A (-3, 5) and B (4, -2), what is the length of AB?
After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.
The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)
Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:
d = √( (4 - (-3))² + (-2 - 5)² )
= √(7² + (-7)²)
= √(98 + 49)
= √147
= 12.124
Therefore, the length of AB is approximately 12.124 units.
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The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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How many tiles can fit in a rectangular floor with length 14 ft and width 6 ft if the the square tiles has an edge of 3/4 ft.
A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.
To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.
Given:
Length of the rectangular floor = 14 ft
Width of the rectangular floor = 6 ft
Edge length of square tile = 3/4 ft
First, let's calculate the number of tiles that can fit horizontally:
Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft
Since we want a whole number of tiles, we need to round down or take the floor value:
Number of tiles horizontally = floor(56/3) = 18 tiles
Next, let's calculate the number of tiles that can fit vertically:
Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft
Again, we round down or take the floor value:
Number of tiles vertically = floor(24/3) = 8 tiles
To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:
Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles
Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.
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24) 28 + 3k < 5(–3 – 8k)
-4 -3
-2
-1
0
2
3
4
5 6
Answer:
k < - 1
Step-by-step explanation:
28 + 3k < 5(-3-8k)
28 + 3k < - 15 - 40k
28 + 15 < - 40k - 3k
43 < - 43k
43/- 43 > k (switch signs because 43 is negative)
k < -1
riya won a LCD TV in amall raffle draw , the tv screen measures 16 inches in height and 12 inches in width. find the hypotenuse of the TV
Solve a/-4 < 1 pls help me
\( \frac{a}{ - 4} < 1 \\ \)
Multiply both sides by - 4
\( \frac{a}{ - 4} \times ( - 4) > 1 \times ( - 4) \\ \)
====================================================
Hint :The direction of the inequalities changes when u multiply or divide the sides by a negative number
====================================================
\(a > - 4\)
\(\huge\text{Answer:}\)
\(\huge\mathrm{a>-4}\)
\(\huge\text{Solution:}\)
Hi there, hope you are having a nice day! :)
Let's solve the given inequality.
\(\rm{\displaystyle\frac{a}{-4} <1\)
First of all, let's get rid of the fraction by multiplying both sides by -4:
\(\rm{a>-4\) (Answer)
_____________
Additional comment
Remember the Golden Rule of Algebra:
Whatever we do to one side, we do to the other.
If we divide one side by -4, we divide the other one by -4 as well.
Also, we flip the inequality sign when we divide by a negative variable.
____________
Hope you find it helpful.
Feel free to ask if you have any doubts.
\(\bf{-MistySparkles^**^*\)
Diana had 41 stickers. She put them in 7 equal groups. She put as many as possible in each group. She gave the leftover stickers to her sister. How many stickers did Diana give to her sister?
Answer:
5 to each group and she gave 6 stickers to he sister
3 ( | -5 |+ | 8 |- | -9 | )
Answer:
66
Step-by-step explanation:
3(5+8+9)
= 3(22)
= 66
If John solved the equation x² - 10x +8=0 by completing the square, one of the steps in his process would
be:
(z-5)² = 17
(z+4)² =10z+16
(z+4)² =10z
(2-5)² = -8
If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.
What is a quadratic equation?In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
x² - 10x + 8 = 0
x² - 10x = -8
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = 8 + (-10/2)²
x² - 10x + 25 = -8 + 25
x² - 10x + 25 = 17
By simplifying, we have;
(x - 5)² = 17
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Question 6
Sharron gets a total of £1050 each month.
She spends 3/10 of this on rent and 2/3 on food and bills.
How much money does Sharron have remaining?
Show your working out and write your answer in the box below.
Solve 5x+4y= 9 for y.
Given:
\(5x+4y=9\)To solve for y:
Explanation:
Isolating 4y, we get,
\(4y=9-5x\)Dividing by 4 into both sides, we get
\(y=\frac{9-5x}{4}\)Final answer:
\(y=\frac{9-5x}{4}\)help!!!!!please!!!!!!!
4x = 64 + 200
what is x
x=66
Step-by-step explanation:
4x = 200 + 64 > 4x = 264 > x= 66
Answer:
x=66
Step-by-step explanation:
Steps
4x=64+200
4x=264
x=66
PLEASE HELP ME!! I really need help
Answer:
(a) 1/6. One out of six sides will give you the desired result.
(b) 3/6. 3 out of 6 sides will give you the desired result.
(c) 2/3. 4 out of 6 sides will give you the desired result.
What is 4 & 1/2+1/8? *
Answer:
4 5/8
Step-by-step explanation:
Rewriting our equation with parts separated
=4+12+18
Solving the fraction parts
12+18=?
Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.
LCD = 8
48+18=58
Combining the whole and fraction parts
4+58=458
How do I do this math questions
\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the Concept of the Area and Volumes.
First we divide this figure in to two shapes , that are Triangle and Rectangle and apply their area formulae.
Total Area = Area of triangle + Area of Rectangle.
Area of triangle = 0.5*b*h
= 0.5*4*5
= 10 sq. units.
---> Area of Rectangle = l*b
= 7*5= 35 sq. units
thus the total area of the Shape is
= 35 + 10= 45 sq. units
PLEASE HELP WILL MARK WILL MARK BRAINLIEST THANK YOU
Answer:
We are given that the frame is 2 units wide, which means that we subtract the length of the outer frame by 2 units for each side:
7 - 2 -2 = 3
9 - 2 -2 = 5
Now, we have the length and width for the smaller rectangle, so we use the area formula (area = length*width) to get:
3*5 = 15
Step-by-step explanation:
Please support my answer.
5x923 pls help plssssss
Answer:
4615
Step-by-step explanation:
5*900=4500
5*20=100
5*3=15
4500+100+15=4615
Boom.
A class has 6 boys and 15 girls. What is the ratio of boys to girls in simplest form?
Answer:
2:5
Step-by-step explanation:
They can both be divided by 3.
6 divided by 3 is 2, while 15 divided by 3 is 5
Boys:Girls
6:15
2:5
Answer:
2:5
Step-by-step explanation:
The coordinates of the vertices of a polygon are shown on the graph below.
What is the name of the polygon?
octagon
pentagon
quadrilateral
triangle
Answer:
Triangle
Step-by-step explanation:
It has three side unlike the others can't have three sides
Which has a value greater than 600 but less than 6,000?
A. 6.1 x 10^3
B. 5.9 x 10^4
C. 5.26 x 10^3
D. 7.87 x 10^3
(look at the picture)
Answer:
c
Step-by-step explanation:
5.26×10³=5260 which is less than 6000 and greater than 600
find the area each sector. Do Not round. Part 1. NO LINKS!!
Answer:
\(\textsf{Area of a sector (angle in degrees)}=\dfrac{\theta}{360 \textdegree}\pi r^2\)
\(\textsf{Area of a sector (angle in radians)}=\dfrac12r^2\theta\)
17) Given:
\(\theta\) = 240° r = 16 ft\(\textsf{Area of a sector}=\dfrac{240}{360}\pi \cdot 16^2=\dfrac{512}{3}\pi \textsf{ ft}^2\)
19) Given:
\(\theta=\dfrac{3 \pi}{2}\)r = 14 cm\(\textsf{Area of a sector}=\dfrac12\cdot14^2 \cdot \dfrac{3\pi}{2}=147 \pi \textsf{ cm}^2\)
21) Given:
\(\theta=\dfrac{ \pi}{2}\)r = 10 mi\(\textsf{Area of a sector}=\dfrac12\cdot10^2 \cdot \dfrac{\pi}{2}=25 \pi \textsf{ mi}^2\)
23) Given:
\(\theta\) = 60°r = 7 km\(\textsf{Area of a sector}=\dfrac{60}{360}\pi \cdot 7^2=\dfrac{49}{6}\pi \textsf{ km}^2\)
When Patricia finished the next level of her video game, she lost 75
points for taking too long and lost 80 points for each of the five targets
she missed. Write the total change to her score as an integer
A A
label required
Answer:
She lost 475 points
Step-by-step explanation:
Given:
Lost point in next level = 75
Number of target = 5
Lost point in each target = 80
Find:
Total changes
Computation:
Total lost points = Lost point in next level + [Number of target][Lost point in each target]
Total lost points = 75 + [5][80]
Total lost points = 75 + 400
Total lost points = 475 point
PLEASEEEE I NEED IT ASAP 51 POINTS IS THE MAX I CAN GIVE PLEASEEEEE HELP ME
Answer:
A
Step-by-step explanation:
2(10+7)
2(17)
=34
Answer:
the answer is a
Step-by-step explanation:
10 times 2 plus 7 times 2=34
Need ANSWER ASAP
Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid.
b) State the following for the transformed function
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
Answer:
See explanation below.
Step-by-step explanation:
Given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Part (a)The parent function of the given function is: y = sin(x)
The five key points for graphing the parent function are:
3 x-intercepts → (0°, 0) (180°, 0) (360°, 0)maximum point → (90°, 1)minimum point → (270°, -1)(See attachment 1)
Part (b)Standard form of a sine function:
\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shift (axis of symmetry: y = D)Therefore, for the given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Amplitude = -2Period = 2π/2 = πPhase shift = 45° to the rightEquation of axis of symmetry: y = 1Part (c)See attachment 2.
Find the area and the circumference of a circle with radius .
Use the value for , and do not round your answers. Be sure to include the correct units in your answers.
Area:
Circumference:
PLS HELP!
Find the volume of this triangular prism.
Be sure to include the correct unit in your answer.
6 cm
9 cm
K
5 cm
Answer:
135cm^3
Step-by-step explanation:
sinA•cosA•tanA+cosA-SinA.cotA give answer pls
Answer:
Step-by-step explanation:
Tan A = Sin A/Cos A
Cot A = Cos A / Sin A
Sin A*Cos A * tan A + Cos A * Sin A * Cot A
\(= Sin A * Cos A * \frac{Sin A}{Cos A} + Cos A*Sin A * \frac{Cos A}{Sin A}\\\\= Sin A * Sin A + Cos A * Cos A\\\\= Sin^{2} A + Cos^{2} A\\\\= 1\)
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)
Identify the surface area of the composite figure to the nearest tenth.
Answer:
D.
Step-by-step explanation:
6a² = surface area for cube
6(5)² = 150
2\(\pi\)(r)(h)+2\(\pi\)r² = surface area cylinder
2\(\pi\)(2)(3)+2\(\pi\)(4) = 20pi
150 + 20pi = 212.8318531
a cyclist and a motorist start from the same point at 8.30 am and travels in opposite directions. the cyclist at 12km and the motorist at 50km/hr,how far apart will they be at 10am
Answer:
Step-by-step explanation:
maths is not my thing
Answer:
If you are looking for the number of faces/sides….
Step-by-step explanation:
1:6
2: 5
3: 8
4:5
5:5
6:5
Hope this helps
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Lmk if its right I’m not sure whether number 2 is 4 or 5
I haven’t done shapes in a while .-.