Answer:
1.75 × 10⁶
Step-by-step explanation:
7,000,000 ÷ 4 = 1750000
Which is 1.75 × 10⁶ in standard form
The sides of the triangular base of prism are 10 cm 8 cm and 6cm respectively and it is 15 cm long .Find the total suface area of the prism.
Answer:
408 cm²
Step-by-step explanation:
the total SA = (2×½×6×8) + (10+8+6)×15
= 48 + 360
= 408 cm²
The total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².
What is a triangular base?In order to create the triangle base, the three triangular sides slant upward. A pyramid with a triangular base is also known as a tetrahedron since it is made up of four triangles.
The shape of a pyramid's base is often used to describe it. A hexagonal pyramid has a base that is a hexagon, as does a triangular pyramid, for example. Pyramids with triangular bases are called triangular pyramids.
A triangle's area is equal to half the sum of its base and height, according to the formula for triangular bases. Whether it be a scalene triangle, an isosceles triangle, or an equilateral triangle, this formula can be used to determine their properties.
The total surface area of the prism calculations are,
b = 6 cm, h = 8 cm, l = 10 cm, and L = 15 cm
[tex]Total\ Surface\ Area = (2\times \frac{1}{2} \times b \times h) + (l+h+b) \times \\ L=(2\times \frac{1}{2} \times 6 \times 8) + (10+8+6) \times 15\\= 48 + 360\\= 408 cm^2[/tex]
Therefore, total surface area of the prism that has a triangular base of 10 cm, 8 cm, and 6cm and it is 15 cm long is 408 cm².
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what is the slope of the graph?
Answer:
The slope is 1.5
Step-by-step explanation:
To get the slope of the graph, we proceed to select any two points lying on the given line, and applying the slope formula
The two selected points are as follows;
(x1,y1) = (-4,0)
(x2,y2) = (-2,3)
m = (y2-y1)/(x2-x1)
m = (3-0)/(-2-(-4)
m = 3/2 = 1.5
Which value of w ww makes 14 = 11 + w 8 ⋅ 6 14=11+ 8 w ⋅614, equals, 11, plus, start fraction, w, divided by, 8, end fraction, dot, 6 a tru
Answer:
w=4
Step-by-step explanation:
Can some help with this problem
Which of the following statements is true?
A) All squares are rectangles.
B) All parallelograms are rectangles.
C) All rhombuses are squares.
D) All rectangles are squares. (D is Not the answer)
[tex]factorise : - \\ \\ 4x {}^{2} - 56x + 196 \\ \\ please \: help \: [/tex]
[tex]\large\bold{\underline{\underline{ 4( {x - 7})^{2} }}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]4x {}^{2} - 56x + 196[/tex]
Take [tex]4[/tex] as the common factor.
[tex] = 4( {x}^{2} - 14x + 49)[/tex]
[tex] = 4( {x}^{2} - 7x - 7x + 49)[/tex]
Taking [tex]x[/tex] as common from first two terms and [tex]7[/tex] from last two terms, we have
[tex] = 4 \: [ x(x - 7) - 7(x - 7) ][/tex]
Taking the factor [tex](x-7)[/tex] as common,
[tex] = 4(x - 7)(x - 7)[/tex]
[tex] = 4( {x - 7})^{2} [/tex]
[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]
On Monday, a localamburger shop said a combined total of 225 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number
of hamburgers sold. How many hamburgers were sold on Monday?
hamburgers
х
?
Answer:
h = hamburgers sold
2h - 72 = 578
2h = 650
2 2
h = 325
There were 72 fewer cheeseburgers sold than hamburgers. That means cheeseburgers = 325 - 72
325 - 72 = 253
253 = cheeseburgers
325 = hamburgers
253 + 325 = 578
Hamburgers = 325
Hope this helps :)
X,Y and Z from a business with capitals Rs 5000,Rs.4500 and Rs.6500 respectively,after 6 month,X doubles has capital and after next 3 months Y trebles his capital .If the profit at the end of the year amount to RS.8300,find the profit obtained by each X,Y and Z.
Answer:
Profit obtained by X = Rs. 2,976.64
Profit obtained by Y = Rs. 2,545.58
Profit obtained by Z = Rs. 2,777.78
Step-by-step explanation:
Total capital for the first 6 months = Rs 5000 + Rs.4500 + Rs.6500 = Rs. 16,000
Total capital for the next 3 months = Rs. 16,000+ Rs 5000 = Rs. 21,000
Total capital for the last 3 months of the year = Rs. 21,000 + (Rs 4500 * 2) = Rs. 30,000
Share of profit of each partner is the sum of all the ratios of his capital to total capital of the business at each point in time multiply by the ratio of the numbers of months covered by each capital to 12 months and then multiply by RS.8300.
Profit obtained by X = ((Rs 5000 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 10,000 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 10,000 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,976.64
Profit obtained by Y = ((Rs 4500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 4500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 13,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,545.58
Profit obtained by Z = ((Rs 6500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 6500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 6,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,777.78
Confirmation of total profit shared = Rs. 2,976.64 + = Rs. 2,545.58 + Rs. 2,777.78 = Rs. 8,300
In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chosen at random from this county, and x are found to be insured against fire. Find the probability distribution for x.
Answer:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]p = 60\%[/tex]
[tex]n = 4[/tex]
Required
The distribution of x
The above is an illustration of binomial theorem where:
[tex]P(x) = ^nC_x * p^x *(1 - p)^{n-x}[/tex]
This gives:
[tex]P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}[/tex]
Express percentage as decimal
[tex]P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}[/tex]
[tex]P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}[/tex]
When x = 0, we have:
[tex]P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}[/tex]
[tex]P(x=0) = 1 * 1 *(0.40)^4[/tex]
[tex]P(x=0) = 0.0256[/tex]
When x = 1
[tex]P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}[/tex]
[tex]P(x=1) = 4 * (0.60) *(0.40)^3[/tex]
[tex]P(x=1) = 0.1536[/tex]
When x = 2
[tex]P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}[/tex]
[tex]P(x=2) = 6 * (0.60)^2 *(0.40)^2[/tex]
[tex]P(x=2) = 0.3456[/tex]
When x = 3
[tex]P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}[/tex]
[tex]P(x=3) = 4 * (0.60)^3 *(0.40)[/tex]
[tex]P(x=3) = 0.3456[/tex]
When x = 4
[tex]P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}[/tex]
[tex]P(x=4) = 1 * (0.60)^4 *(0.40)^0[/tex]
[tex]P(x=4) = 0.1296[/tex]
So, the probability distribution is:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.
Answer:
There is a non-removable discontinuity at x = 3
Step-by-step explanation:
We are given that
[tex]f(x)=\frac{x^2+9}{x-3}[/tex]
We have to find true statement about given function.
[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]
=[tex]\infty[/tex]
It is not removable discontinuity.
x-3=0
x=3
The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.
Therefore, x=3 is non- removable discontinuity of function f(x).
Hence, option B is correct.
Pls solve last question pls pls
Answer:
i don't know how to work this
Answer:
x = [tex]\frac{3}{4}[/tex] , x = 20
Step-by-step explanation:
2([tex]\frac{3x-5}{x+2}[/tex] ) - 5 ([tex]\frac{x+2}{3x-5}[/tex] ) = 3
Multiply through by (x + 2)(3x - 5) to eliminate the fractions
2(3x - 5)² - 5(x + 2)² = 3(x + 2)(3x - 5) ← expand factors on both sides
2(9x² - 30x + 25) - 5(x² + 4x + 4) = 3(3x² + x - 10) ← distribute parenthesis
18x² - 60x + 50 - 5x² - 20x - 20 = 9x² + 3x - 30 ← simplify left side
13x² - 80x + 30 = 9x² + 3x - 30 ( subtract 9x² + 3x - 30 from both sides )
4x² - 83x + 60 = 0 factor by splitting the x- term
4x² - 80x - 3x + 60 = 0
4x(x - 20) - 3(x - 20) = 0
(4x - 3)(x - 20) = 0
Equate each factor to zero and solve for x
4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]
x - 20 = 0 ⇒ x = 20
Help and explain please and thank you !!!!!!!
Answer:
[tex]q = 3[/tex]
Step-by-step explanation:
[tex]3q−2=7[/tex]
[tex]3q=7+2[/tex]
[tex]3q=9[/tex]
[tex]q = \frac{9}{3} [/tex][tex]q = 3[/tex]
Hope it is helpful....Write 8 as the ratio of two integer
Answer:
Step-by-step explanation: 7 1 16 37
8/1 8 divided by 1
16/2 16 divided by 2
24/3 24 divided by 3 I could go on, but won't
Porfavor necesito ayuda en esto.
Es para hoy :(
Answer:
17
Step-by-step explanation:
[tex]solve : - \\ \\ (4 {}^{2} + 5 {}^{2} ) = {?}[/tex]
Step-by-step explanation:
4² = 16
5² = 25
16+25 = 41
41 is the answer.
Hope it helps! :)
Answer:
[tex]( {4}^{2} + {5}^{2} ) \\ (16 + 25) \\ = 41[/tex]
the question please i need help
Answer:
90g strawberry jelly
6 sponge fingers
315ml custard
135g tinned fruit
Step-by-step explanation:
----------------------------------------
Since those ingredients that are in the question say making a trifle for four people, let's divide each ingredient by four to find the ingredients for one person, and multiply by 3 to find the ingredients for 3 people.
So,
[tex]120/4=30[/tex]g strawberry jelly
[tex]8/4=2[/tex] sponge fingers
[tex]420/4=105[/tex]ml custard
[tex]180/4=45[/tex]g tinned fruit
There are the ingredients to make a trifle for one person.
-------------------->>>>
Now, let's multiply each of the ingredients for one person and multiply that by three to find the ingredients needed to make a trifle for four people.
[tex]30*3=90[/tex]g strawberry jelly
[tex]2*3=6[/tex] sponge fingers
[tex]105*3=315[/tex]ml custard
[tex]45*3=135[/tex]g tinned fruit
These are the ingredients needed to make a trifle for three people.
----------------------------------------
Hope this is helpful.
Gabe went out to lunch with his best friend. The bill cost $16.40 before tax and tip. He paid a 9% tax and he left a 20% tip. How much did Gabe spend?
Hint: Tax and tip are both based on the original cost of the bill.
Don't forget to round to the nearest cent!
Someone please help me with this algebra problem
Answer:
90
Step-by-step explanation:
Solve by factorisation.
3x² + 10x - 8 = 0
Answer:
3x²+12x-2x-8. = 0
3x(X+4)-2(X+4) = 0
(x+4)(3x-2) =0
[tex]x = (- 4) \: or \: x = \frac{2}{3} \: are \: the \: solutions[/tex]
What is the value of x?
0 14
0 17
O 27
O 34
PLEASE HELP
Hi need help with this so plz help me
PLEASE HELP! Which point would be included in the solution set of this system of inequalities?
A. (-2,10)
B. (2,10)
C. (0,0)
D. (-2,-10)
Answer:
D
Step-by-step explanation:
-10 < -6 - 1
-10 < - 7 (ok)
-10 < -4 - 3
-10 < -7 (ok)
The answer is D (-2, -10)
x + 2y when x = 1 and y = 4
Answer:
9
Step-by-step explanation:
x = 1
y = 4
x + 2y = 1 + 8 = 9
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
9
Step-by-step explanation:
x + 2y
subtitute:
1 + 2(4)
simplify:
1 + 8 = 9
A number ending in ___ is never a perfect square.
Answer:
2, 3, 7 or 8
Step-by-step explanation:
A bottling company marks a 0 for every bottle that comes out correct and a 1 for every defective bottle. Estimate the probability that the next bottle is defective
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]0 \to[/tex] Correct
[tex]1 \to[/tex] Defective
Required
The probability that the next is defective
The question is incomplete because the list of bottles that came out is not given.
However, the formula to use is:
[tex]Pr = Num ber\ o f\ d e f e c t i v e \div T o t a l\ b o t t l e s[/tex]
Take for instance, the following outcomes:
[tex]0\ 1\ 0\ 0\ 0\ 1\ 0\ 0\ 1\ 1\ 0\ 0\ 0\ 1[/tex]
We have:
[tex]Total = 14[/tex]
[tex]D e f e ctive = 9[/tex] --- i.e. the number of 0's
So, the probability is:
[tex]Pr = 9 \div 14[/tex]
[tex]Pr = 0.643[/tex]
Answer:
1/20
Step-by-step explanation:
000000000000100000
It is asking the probability of a defective bottle
there is one defective bottle out of 20
Determine the area of an obtuse triangle with a height
of 11 cm and a base of 22 cm
Step-by-step explanation:
A
=
h
b
b
2
=
11
·
22
2
=
121
cm²
The area of the obtuse triangle with a height of 11 cm and a base of 22 cm is 121 cm².
To determine the area of an obtuse triangle, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
In this case, the height of the triangle is given as 11 cm and the base is given as 22 cm.
Substituting these values into the formula, we have:
Area = (1/2) * 22 cm * 11 cm
Calculating this expression, we get:
Area = (1/2) * 242 cm²
Simplifying further, we have:
Area = 121 cm²
The area of a triangle is calculated by multiplying half of the base by the height. In this case, the given height is 11 cm and the base is 22 cm. Substituting these values into the formula, the area of the obtuse triangle is calculated to be 121 cm².
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which equation represents a line parallel to the y-axis?
Answer:
B. x=4
Step-by-step explanation:
I hope this helps!
Need help on this question asap pleasee
Answer:
I believe its the 1st answer.
HELP HELP HELPPPP PLEASEEE
Directions: Determine if segments AB and CD are parallel, perpendicular, or neither.
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Given:
AB formed by (-2,13) and (0,3).
CD formed by (-5,0) and (10,3).
To find:
Whether the segments AB and CD are parallel, perpendicular, or neither.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
AB formed by (-2,13) and (0,3). So, the slope of AB is:
[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]
[tex]m_1=\dfrac{-10}{2}[/tex]
[tex]m_1=-5[/tex]
CD formed by (-5,0) and (10,3). So, slope of CD is:
[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]
[tex]m_2=\dfrac{3}{10+5}[/tex]
[tex]m_2=\dfrac{3}{15}[/tex]
[tex]m_2=\dfrac{1}{5}[/tex]
Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.
[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]
[tex]m_1\times m_2=-1[/tex]
Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.
Hence, the segments AB and CD are perpendicular.
Answer:
AB is perpendicular to CD.
Step-by-step explanation:
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Slope of a line passing through two points is
[tex]m= \frac{y''-y'}{x''- x'}[/tex]
The slope of line AB is
[tex]m= \frac{3- 13}{0+2} = -5[/tex]
The slope of line CD is
[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]
As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High frequency EM is thought to be a cause of cancer; the lower frequencies associated with household current are generally assumed to be harmless. The following table summarizes the probability distribution for cancer sufferers and their wiring configuration in the Denver area.
Leukemia Lymphoma Other Cancers
High Frequency wiring 0.242 0.047 0.079
Low frequency wiring 0.391 0.098 ???
(a) What is the missing probability (labelled ???) in the above table?
(b) What is the probability of having high frequency wiring among cancer suffers in the Denver area?
(c) Is the event "Having Leukemia" independent of the event "Having high frequency frequency wiring"? Explain.
Answer:
[tex]x = 0.143[/tex]
[tex]P(High\ |\ Cancer) = 0.215[/tex]
Not independent
Step-by-step explanation:
Given
See attachment for proper table
Solving (a): The missing probability
First, we add up the given probabilities
[tex]Sum = 0.242+0.047+0.079+0.391+0.098[/tex]
[tex]Sum = 0.857[/tex]
The total probability must add up to 1.
If the missing probability is x, then:
[tex]x + 0.857 = 1[/tex]
Collect like terms
[tex]x = -0.857 + 1[/tex]
[tex]x = 0.143[/tex]
Solving (b): P(High | Cancer)
This is calculated as:
[tex]P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}[/tex]
So, we have:
[tex]P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}[/tex]
[tex]P(High\ |\ Cancer) = \frac{0.079}{0.368}[/tex]
[tex]P(High\ |\ Cancer) = 0.215[/tex]
Solving (c): P(Leukemia) independent of P(High Wiring)
From the attached table
[tex]P(Leukemia\ n\ High\ Wiring) = 0.242[/tex]
[tex]P(Leukemia) = 0.242 + 0.391 =0.633[/tex]
[tex]P(High\ Wiring) = 0.242+0.047+0.079=0.368[/tex]
If both events are independent, then:
[tex]P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)[/tex]
[tex]0.242 = 0.633 * 0.368[/tex]
[tex]0.242 \ne 0.232[/tex]
Since the above is an inequality, then the events are not independent
