Answer:
£105.04
Step-by-step explanation:
To round an amount to the nearest cent, check the value of its thousandths. If the value is equal to 5 or greater, increase the value in the cent’s place by 1 and then remove all digits to the right after the second decimal place. If the value is equal to 4 or less, simply remove all the digits to the right after the second decimal place. For example with £105.035 the thousandths’ value is 5, so we round up: £105.035 --> £105.04
A'BC' is a dilation of ABC.
If the center of dilation was (0,0), what was the scale factor used to create the dilation?
Answer:
4
Step-by-step explanation:
ill explain it in the comments but trust me that is the answer
The population of the world in 1987 was about 5 billion, and the relative growth rate was estimated at about 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1992. Round your answer to 2 decimal places.
The world population in 1992 is projected to be ? billion people.
Answer:
Step-by-step explanation:
Given that the formula for exponential calculation :
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
A = final amount
P = initial principal balance
r = increasing rate
n = number of times increases applied per time period
t = number of time periods elapsed
[tex]A = 5,000,000,000(1 + \frac{2}{100})^{5}\\A = 5,000,000,000(\frac{100}{100} + \frac{2}{100})^{5}\\A = 5,000,000,000(\frac{102}{100})^{5}\\A = 5,000,000,000(\frac{51}{50})^{5}\\A = 5,000,000,000(1.104)\\\\A = 5,520,000,000\\A = 5.52billion[/tex]
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Determine the state income taxes on a graduated income tax basis: Maurice Jordan's annual salary as a motorcycle mechanic is $18,750.00 paid in 26 pay periods. He is married.
Based on the state income tax rates, and Maurice's annual salary, he state income tax for Maurice is $820.63
How to find the state income taxes?Maurice earns $18,750.00 per year so will have state income taxes of:
= (3,000 x 2%) + ((5,000 - 3,000) x 3%) + ((17,000 - 5,000) x 5%) + ((18,750 - 17,000) - 5.75%)
The state income tax is therefore:
= (3,000 x 2%) + ((5,000 - 3,000) x 3%) + ((17,000 - 5,000) x 5%) + ((18,750 - 17,000) - 5.75%)
= 60 + 60 + 600 + 100.625
= $820.63
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Write the function (x−6)2=81 in standard form.
The standard form given of the function is x² - 12x - 45.
What is the standard form of quadratic equation?A quadratic equation has the conventional form ax2 + bx + c = 0, where an is the leading coefficient and a real integer that is not zero.
The quadratic equation ax2 + bx + c = 0 has the conventional form, where a 0 and a, b, and c are real values.
The given function is -
(x−6)²=81
⇒ x² + 36 - 12x = 81
⇒ x² - 12x = 81 - 36
⇒ x² - 12x = 45
⇒ x² - 12x - 45
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Lorie ordered a shed to hold her gardening supplies. The shed had a length of 18.25 ft, a width of 15 ft, and a height of five and one fifth ft.
Determine the volume, V, using the formula V = lwh.
1,423.5 cubic ft
1,373.5 cubic ft
142.35 cubic ft
38.45 cubic ft
The volume (V) of Lorie's shed, being 18.25 ft in length, 15 ft in width and (5 1/5) ft in height, will be 1423.5 cubic fts.
As per the question statement, Lorie ordered a shed of length 18.25 ft, width 15 ft and height (5 1/5) ft, to hold her gardening supplies.
We are required to calculate the volume of the above mentioned shed using the formula, provided in the question statement itself.
To solve this question, we will simply put our values in the provided formula and calculate to obtain our desired answer.
Here, "l" = 18.25 ft
"w" = 15 ft,
And "h" =(5 1/5) =(25+1)/5=26/5=5.20ft.
Substituting the values of "l", "w" and "h" in the formula (V = lwh), we get,
Volume of the shed (V) = 18.25[tex]\times[/tex] 15 [tex]\times[/tex] 5.20
[tex]or, V = 1423.5ft^{3}[/tex].
Volume: It is a measure of occupied three-dimensional space by an object or a substance, or that is enclosed within a container.
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Write the equation of each line in slope-intercept form.
The line parallel to y=-3x + 4 that passes through (9,-6).
O y = 3x + 21
Oy=-3x+4
Oy=-1/3x + 27
Oy=-3x + 21
The fourth option:
y=-3x+21 is correct.
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-3} x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -3 and that it passes through (9 , -6)
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{9}) \implies y +6= -3 (x -9) \\\\\\ y+6=-3x+27\implies {\LARGE \begin{array}{llll} y=-3x+21 \end{array}}[/tex]
Out of 120 students, 32 play football only. 8 played both football and volley ball. The number of players who played volley hall is twice the number of players who played football. Using a diagram find the number of students who played volleyball only and who didn't play both games
Answer:
64 students played volly ball, 24 students played both football and vollyball
Step-by-step explanation:
srry if its not correct but im 70% sure it is
Can somebody help me write this in standard notation?
Answer:
6400
Step-by-step explanation:
the exponent of the ten is the number of decimal spaces you move.
6.4(103)
=6.4*103
=6.4*(10*10*10)
=6400
Below is the graph h(x)h(x)h, left parenthesis, x, right parenthesis. The function intersects its midline at (0.5,-3)(0.5,−3)left parenthesis, 0, point, 5, comma, minus, 3, right parenthesis and has a minimum point at (-1.5,-8)(−1.5,−8)left parenthesis, minus, 1, point, 5, comma, minus, 8, right parenthesis. Find a formula for h(x)h(x)h, left parenthesis, x, right parenthesis. Give an exact expression
The sine function h(x) is given by:
h(x) = 5sin(π/4(x - 0.5)) - 3.
What is the sine function?The cosine function is defined as follows:
g(x) = asin(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.For this function, we have that:
The midline is of -3.The minimum value is of -8.Hence the coefficient a is of 5, as:
a = -3 - (-8) = -3 + 8 = 5.
A standard cosine function with amplitude 5 would vary between -5 and 5, with midline at 0, hence the coefficient d is of d = -3.
The minimum value and midline form one-fourth the period, hence, since the period is of 4 x (0.5 - (-1.5)) = 8, we have that:
2π/B = 8
B = π/4
The standard midline is at x = 0, but for this function function it is at x = 0.5, meaning that the function was shifted 0.5 units right, hence c = -0.5.
Thus the function is given by:
h(x) = 5sin(π/4(x - 0.5)) - 3.
The graph at the end of the answer shows that the function has the desired features.
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Use lineR regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places . Write your final answer in a form of an equation y=mx+b
X 1. 2. 3. 4. 5. 6
Y 77. 101. 118. 137. 158. 194
The equation for the linear function that best fits the data is y = 22.14x + 53.33
How to use lineR regression to find the equation for the linear function that best fits the data?The data is given as
X 1. 2. 3. 4. 5. 6
Y 77. 101. 118. 137. 158. 194
Next, we enter the above values in a graphing calculator
From the graphing calculator, we have the following calculatiion summary:
Sum of X = 21Sum of Y = 785Mean X = 3.5Mean Y = 130.8333Sum of squares (SSX) = 17.5Sum of products (SP) = 387.5For the regression equation, we have
y = bx + a
Where
b = SP/SSX = 387.5/17.5 = 22.14286
a = MY - bMX = 130.83 - (22.14*3.5) = 53.33333
Approximate b and a
So, we have
b = 22.14
a = 53.33
This gives
y = 22.14x + 53.33
Hence, the equation for the linear function that best fits the data is y = 22.14x + 53.33
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what is the reciprocal of 4/8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4}{8}}\\\\\mathsf{= \dfrac{8}{4}}\\\\\mathsf{= \dfrac{8\div4}{4\div4}}\\\\\mathsf{= \dfrac{2}{1}}\\\\\mathsf{= 2\div1}\\\\\mathsf{= 2}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{2\ or\ \dfrac{8}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Answer:
Reciprocal of 4/8 = 8/4
Step-by-step explanation:
To get the reciprocal of 4/8 based on that definition, we can make the following equation where "R" is the reciprocal of 4/8.
(4/8) × R = 1
When we solve for R, we get the answer to the reciprocal of 4/8 as a fraction as follows:
(4/8) × R = 1
R = 8/4
Reciprocal of 4/8 = 8/4
Multiple choice & will mark brainest!
Factor the polynomial: Factor the expression below x^2 +6+9
A: (x-3)(x-3)
B: (x+3)(x+3)
C: 3(x+3)(x+3)
Answer:
x^2 + 15
Step-by-step explanation:
All the other answers are wrong
Select the correct answer from each drop-down menu. Expand the binomial (2x^2+y^2)^4 Fill in the missing coefficients in the expansion of the binomial
The expansion of the binomial (2x² + y²)⁴ is;
(2x² + y²)⁴ = 16x⁸ + 32x⁶y² + 24x⁴y⁴ + 8x²y⁶ + y⁸
What is Binomial expansion?
The binomial expansion describe the algebraic expansion of powers of a binomial.
The expression is given as;
(2x² + y²)⁴
Now, The expansion of binomial is;
(2x² + y²)⁴ = (2x²)⁴ + 4 * (2x²)³ * y² + 6 * (2x²)² * (y²)² + 4 * 2x² * (y²)³ + (y²)⁴
= 16x⁸ + 32x⁶y² + 24x⁴y⁴ + 8x²y⁶ + y⁸
Hence, The expansion of the binomial (2x² + y²)⁴ is;
(2x² + y²)⁴ = 16x⁸ + 32x⁶y² + 24x⁴y⁴ + 8x²y⁶ + y⁸
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Which is one of the transformations applied to the graph of f(x)=x2 to produce the graph of g(x)=2x2−28x+3?
The transformations applied to the graph of f(x)=x2 to produce the graph of g(x)=2x2−28x+3 is f(x) shifting right 7 units
This is further explained below.
Which is one of the transformations applied to the graph of f(x)=x2 to produce the graph of g(x)=2x2−28x+3?Generally, the equation for vertex form is mathematically given as
g(x) = 2(x – 7)2 – 95
Using the translations rule:
The conclusion that can be drawn from the vertex form " 2(x – 7)2 – 95" is that the parent function f(x) has been relocated 7 units to the right and 91 units upward.
In conclusion, we can say that f(x) shifted right 7 units
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The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.
Answer:
The numbers are 25 & 55
Step-by-step explanation:
You can quantify this problem by using x to take the place of the first number. Because x is multiplied by 2 we get 2x, and add 5 since it is 5 more than twice the first. We can add x to 2x+5 which is 3x+5 and set it equal to 80. Then solve for x to get your first number, and subtract 80 from x to get your second number. Your work should look like this.
[tex]x + 2x + 5 = 80\\3x + 5 = 80\\3x = 80-5\\3x = 75\\3x/3 = 75/3\\x = 25\\80 -25 = 55[/tex]
Hope this helps!
What is the sum of the 3rd cube number and the 5th cube number?
Answer:
152
Step-by-step explanation:
you will multiply 3and 5 each three times.
3*3*3=27
5*5*5=125
27+125=152
Please help me with this
Answer:21 decrees
Step-by-step explanation:
i gotch you
If someone drives an average of 23,000 miles per year, how many gallons will he save in a year by increasing his tire pressure from 30 to 35 psi?
If someone drives an average of 23,000 miles per year, the number of gallons he will save in a year by increasing his tire pressure from 30 to 35 psi is: 32 gal.
Number of gallons savedFirst step is to find the number of gallon consumed at each pressure
30 psi=23,000/20.5 mpg
30 psi = 1,121.95 gal
35 psi=23, 000/ 21.1 mpg
35 psi =1,090.05 gal
Now let determine the gallon saved
Gallons saved = 1,121.95 gal- 1,090.05 gal
Gallons saved=31.9 gal
Gallons saved=32 gal (Approximately)
Therefore If someone drives an average of 23,000 miles per year, the number of gallons he will save in a year by increasing his tire pressure from 30 to 35 psi is: 32 gal.
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The complete question is:
When a car's tire pressure is 30 pounds per square inch (psi), it averages 20.5 mpg of gasoline. If the tire pressure is increased to 35 psi, the car averages 21.1 mpg of gasoline.
If someone drives an average of 23,000 mi per year, how many gallons of gasoline will he save in a year by increasing his tire pressure from 30 to 35 psi?
Using long division what is the answer to 6.64 / 8.3?
Answer:
Step-by-step explanation:
Hey, don't worry, I got you! The answer is 0.8
The answer of 6.64 / 8.3 = 0.800
How do you do long division with decimals?When dividing a decimal by a whole number, use the same long division method as when doing so with two whole numbers, but place the decimal point in the answer exactly where it appears in the dividend. Add a 0 to the end of the payout and keep dividing until there is no remainder if it doesn't divide evenly.To convert these decimal numbers into whole numbers, the first step is to multiply each value by 10. Counting backwards from 3.5, we arrive at 35. The other number in our phrase, 15.75, cannot simply be multiplied by 10 once, as can be shown by looking at it. The result would be 157.5, which is still not a perfect number.Calculations :
We then have the equations:
66.4 ÷ 83 = 0.800
and therefore:
6.64 ÷ 8.3 = 0.800
Both calculated to 3 decimal places.
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Find the inverse of g (x)=1/3x-7 and the. Find it’s domain and range
Im unsure, I just took this test :P
Kate read 3 1/2 pages in 1/6 of an hour. At this rate, how many pages will she read in an hour?
[tex] \huge \sf { \star{ \green{ \underbrace{\overbrace{\blue{Answer}}}}}}{\star} \\ \\ \: \: \sf \rightarrow{\fbox{21 \: \: Pages}}[/tex]
Step-by-step explanation:
[tex]\texttt{Kate reads} \\ \: \rightarrow \: \tt \: 3 \frac{1}{2} in \: \frac{1}{6} \texttt{ of an hour} \\ \\ \rightarrow 3 \: \frac{1}{2} or \frac{7}{2} \\ \\ \tt = 3.5 \: \texttt{pages in } \frac{1}{6} \texttt{of an hour} \\ \\ \frac{1}{6} = \frac{10 \: min}{60 \: min} \\ \\ \therefore \: 3.5 \: pages \: in \: 10 \: min \: \\ \\ \: \: multiply \: \: 3.5 \: \: by \: \: 6 \: times \: \: \\ \: \: \\ \\ = > 3.5 \times 6 \\ \\ \ = > \blue{\fbox{\pink {21 \tt pages}}}[/tex]
Kate will read 21 pages at the same ratio as much as in 3 1/2 pages in 1/6 of an hour.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Given that,
Kate read 3 1/2 pages in 1/6 of an hour.
1/6 hour → 3 1/2 pages
→ 3 + 1/2 pages
→ 7/2 pages
Multiply by 6 on both sides,
1 hour → (7/2) × 6 = 21 pages
Hence "Kate will read 21 pages at the same ratio as much as in 3 1/2 pages in 1/6 of an hour".
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9,513 nearest thousands
9,513 rounded off to nearest thousands = 10,000
we have given a four digit number 9,513 to round off to nearest thousands.
steps that should be followed for rounding numbers to the nearest thousand:
Mark the number that we need to round. In this case, we will mark the digit in the thousands place. This rounding digit will be the one that will eventually be affected.Since we are rounding to the nearest thousand, we need to check the digit to the immediate right of the thousands place, that is the hundreds place.If the digit in the hundreds place is less than 5, we do not change the digit in the thousands place. However, all the digits to the right of the thousands place are changed to 0.If the digit in the hundreds place is 5 or more than 5, we increase the thousands place by 1, and all the digits to the right of the thousands place are changed to 0.round 9,513 to nearest thousands:
∵ hundreds place is 5
∴9,513≈10,000
hence, 9,513 nearest thousands is 10,000
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HELP SORRY AGAIN I JUST DONT UNDERSTAND SCHOOL
[tex]area = length \times width \\ 35 = length \times 5 \\ length = \frac{35}{5} = 7[/tex]
An atom of gold has a mass of approximately 3.25×10−22 grams. What is the mass of 4000 atoms of gold? Express your answer in scientific notation.
Taking into account the rule of three, the mass of 4000 atoms of gold is 1.3×10⁻¹⁸ grams.
Rule of threeThe rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
If the relationship between the magnitudes is direct, the direct rule of three must be applied as follow, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: x= (c×b)÷a
Mass of 4000 atoms of goldYou can apply the following rule of three: if 1 atom of gold has a mass of approximately 3.25×10⁻²² grams, 4000 atoms of gold have how much mass?
mass= (4000 atoms× 3.25×10⁻²² grams)÷ 1 atom
mass= 1.3×10⁻¹⁸ grams
Finally, the mass of 4000 atoms of gold is 1.3×10⁻¹⁸ grams.
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What is the interquartile range of the lengths of bananas?
Answer:42/80
Step-by-step explanation:
We know that the shop only buys abanans with lengths between 13 cm and 20 cm.So, the fraction of the 80 bananas is actually a ratio between the y-values of each lenth (13 and 20 cm) and the total 80. First, let's see which y-values belong to each length.Notice that 13 belons to 20 at Cumulative Frequency. And 20 belongs to 62. So, the pairs are (13,20) and (20,62).This fraction means that the shop only buys 42 bananas out of 80, because those are between 13 cm and 20 cm.
The solution is: the interquartile range of the lengths of bananas is between 13 cm and 20 cm.
What is interquartile range?In descriptive statistics, the interquartile range tells you the spread of the middle half of your distribution. Quartiles segment any distribution that's ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.
We know that the shop only buys bananas with lengths between 13 cm and 20 cm.
So, the fraction of the 80 bananas is actually a ratio between the y-values of each length (13 and 20 cm) and the total 80.
First, let's see which y-values belong to each length.
Notice that 13 belongs to 20 at Cumulative Frequency.
And 20 belongs to 62.
So, the pairs are (13,20) and (20,62).
This fraction means that the shop only buys 42 bananas out of 80,
because those are between 13 cm and 20 cm.
Hence, The solution is: the interquartile range of the lengths of bananas is between 13 cm and 20 cm.
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Find the equation of a line parallel to y−7=−3x that passes through the point (-6,6)
Answer:
y = -3x - 12
Step-by-step explanation:
y - 7 = -3x Put in the slope intercept form for a line
y = -3x + 7
Use the slope (-3), the x(-6) and the y(6) to find the y intercept and to write the equation for the line.
y = mx + b
6 = (-3)(-6) + b
6 = 18 + b Subtract 18 from both sides
-12 = b
y =mx + b
y = -3x -12
Solve the equation v=-3x+s for the variable w
The equation has no solution for the variable w
How to solve the equation for w?The equation is given as
v = -3x + s
In the above equation, there is no occurrence of the variable w
This means that it is not possible to solve the equation for w
Hence, the equation has no solution for the variable w
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Maria practiced the piano for 2 1/2 hours last week and 1 3/4 hours this week.Use the bar diagram sections to construct a bar diagram that represents how many hours Maria practiced in the past 2 weeks.
How many hours did Maria practice the piano in the past 2 weeks?
The number of hours that Maria practiced in the past 2 weeks will be 4 1/4 hours.
How to illustrate the fraction?From the information, Maria practiced the piano for 2 1/2 hours last week and 1 3/4 hours this week.
Therefore, the number of hours that Maria practiced in the past 2 weeks will be:
= 2 1/2 + 1 3/4
= 2 2/4 + 1 3/4
= 4 1/4 hours
The number of hours that Maria practiced in the past 2 weeks will be 4 1/4 hours.
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what is 0.015 X 15 show ur work and 0.45 X 45 show ur work for both.
It is estimated that 78% of drivers use their turn signal.
Part A: What is the probability that exactly 3 drivers use their turn signal if a police
officer pulls over five drivers? (5 points)
Part B: What is the probability the next driver using their turn signal that the police
officer pulls over is the fifth driver? (5 points) (10 points)
I
Answer:
A) 0.23
B) 0.14
Step-by-step explanation:
Part A)
To solve this question, we'll have to use the Bernoulli formula.
The formula claims that the probability to get [tex]k[/tex] successes out of [tex]n[/tex] attempts is given by [tex]\binom{n}{k}p^k(1 - p)^{n - k}[/tex].
In our case, [tex]n = 5[/tex], [tex]k = 3[/tex], and [tex]p = 0.78[/tex].
Therefore, the probability that 3 out of the 5 drivers use their turn signal is
[tex]\binom53 \times 0.78^3 \times 0.22^2 \to 0.23[/tex]
Part B)
We are told that the police officer pulled over 5 drivers, 3 of them using turn signals. In this part, we are asked "what is the probability that the 5th driver uses the turn signal and only 2 of the previous four drivers use turn signals?".
[tex]0.78 \times \binom42 \times 0.78^2 \times 0.22^{4-2}\\\to 0.14[/tex]