In order to determine the price per orange, calculate the quotient in between 3.78 and 14:
3.78/14 = 0.27
Hence, one orange costs $0.27
If Sandy's gross pay is $750 weekly, what is her annual salary?
weekly pay = 750
There are 48 weeks in a year.
To calculate the annual salary multiply the weekly gross pay by the number of weeks in a year:
750 x 48 = $36,000
Consider the expression 7x^2 + 12x - 4. Select two correct expressions that are factors of the expression. A) (7x-2)B) (x+2) C) (7x+2) D) ( x -2) E) (3x-4) F) (4x-1) G) (4x+1)H) (x - 4)
The given expression is a quadratic expression. We would simplify by applying the factorisation method. We would determine two numbers whos sum or difference is 12 and whose product is - 28. These numbers are 14 and - 2. It becomes
[tex]\begin{gathered} 7x^2+12x-4 \\ 7x^2+14x-2x-4 \\ 7x(x+2)-2(x+2) \\ (7x-2)(x+2) \end{gathered}[/tex]The correct options are
A) (7x - 2)
B) ((x + 2)
Calculate the length of the bolded arc. Round your answer to the nearest hundredth (two decimal places). No units are needed.
The length of arc is given as:
[tex]\begin{gathered} \text{length of arc = }\frac{\theta}{360}_{}\times2\times\pi\times r \\ r\text{ is the radius of the circle} \\ \\ \theta=165^0 \\ r=11ft \end{gathered}[/tex]Therefore, we can solve for the length of the arc:
[tex]\begin{gathered} \text{length of arc =}\frac{165}{360}\times2\times\pi\times11=10.0833\pi \\ \text{length of arc=31.6777ft}^2 \\ \\ To\text{ the nearest hundredth:} \\ \text{length of arc = 31.68ft}^2 \end{gathered}[/tex]A local bakery has determined the probability distribution for the number of cheesecake that they sell in a given date that X = number of cheesecake sold on organismly selected day
Having the probability distribution in the range from 0 to 20, the sum of all probabilities should give 1. This will be useful to estimate the missing value (P(x = 15)).
Let's establish the sum of probabilities:
[tex]P(x=0)+P(x=5)+P(x=10)+P(x=15)+P(x=20)=1[/tex]Now, we can replace values and solve for P(x = 15):
[tex]0.11+0.3+0.21+P(x=15)+0.1=1[/tex][tex]0.72+P(x=15)=1[/tex][tex]\begin{gathered} P(x=15)=1-0.72 \\ P(x=15)=0.28 \end{gathered}[/tex]The probability of selling 15 cheesecakes on a given day is 0.28 (28%)
Now, to estimate the probability of selling at least 10 cheesecakes can be calculated by summing the probabilities of selling 10, 15, or 20. In this case, we include the 10 because it says at least. Then:
[tex]P(x\ge10)=P(x=10)+P(x=15)+P(x=20)[/tex]Replacing values:
[tex]P(x\ge10)=0.21+0.28+0.1[/tex][tex]P(x\ge10)=0.59[/tex]The probability of selling at least 10 is 0.59 (59%))
what is the answer to -4=r-6solve for r
-4 = r-6
Add 6 to both sides of the equation:
-4+6 = r-6+6
2 = r
r=2
10tY -10 10 -10 Match the function with the graph. a =Inx+3 --in C. b. =n- 3 d y=-n(x+ 3) -1 AL-
The function that matches the graph above is -ln(x+3). The answer is option d.
As we can see, the ln(x) has a transformation since it was multiplied by -1 (changing its direction), and is shifted three units to the left, represented by (x+3). We have to remember that the ln(x) function passes through the point (1, 0), and shifted three units to left makes the function passes through the point (-2, 0) (this is the x-intercept).
i have to use trig ratios to find the unknown angle measurement or side length.
In order to find x, we apply the trigonometric ratio
Given:
[tex]\begin{gathered} \text{angle, }\theta=57^0 \\ \text{adjacent = x} \\ \text{hypotenuse}=10 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \cos 57^0=\frac{\text{ adjacent}}{\text{ hypotenuse}}=\frac{x}{10} \\ \cos 57^0=\frac{x}{10} \\ x=10\times\cos 57^0 \\ x=10\times0.5446 \\ x=5.446 \end{gathered}[/tex]Therefore, the value of x, the adjacent side is 5.45 units to the nearest hundredth
help me please
thank you
Answer: The option is true.
Step-by-step explanation:
The value of x is greater than '-3' and less than '7'. And, the only option C is showing the interval rightly. In interval notation, we'll write it in small brackets like:
(-3,7)
PLS HELP!! Which of the following conjunctions matches the graph?
6≤y+3≤8
6≤y-3≤8
6≥y-328
None of the choices are correct.
A mathematical phrase in which the sides are not equal is referred to as being inequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
here, conjunctions matches the graph is 6 ≥y-3 ≥ 8
What is inequality ?a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.A mathematical phrase in which the sides are not equal is referred to as being inequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.Long-term social and economic development is under danger due to inequality, which also harms property reduction and undermines people's sense of fulfillment and self-worth. Crime, sickness, and environmental destruction can all result from this.To learn more about : Inequality
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Select all the correct answers.
A triangular frame has two side lengths measuring 18 inches and 12 inches. Which values are possible lengths for the third side?
20 in
32 in
28 in
6 in
24 in
30 in
As per the Pythagoras theorem, the possible length of the third side are 30 or 32.
Pythagoras theorem:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Given,
A triangular frame has two side lengths measuring 18 inches and 12 inches.
Here we need to find the possible length of the third sides.
WE know that, the third side of a must be greater than the sum of the other two sides.
So, we have to add the given sides then w get get the value,
=> 18 + 12
=> 30.
So, therefore, the third side must be greater than 30.
From the given options the possible values of the third side are 30 and 32.
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Answer:24 in. 28in. 20in.
Step-by-step explanation:
If the population of Alaska in 2000 was
622,000 and 733,000 in 2020, assuming
exponential growth, what would the
population be in 2050?
[?] people
Using mathematical operations, the population of Alaska in 2050 will be 8,99,500.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, the population in 2050:
Population increases from 2000 to 2020:733,000 - 622,000 = 1,11,000Population change in 20 years = 1,11,000In 10 years = 1,11,000/2 = 55,500So, poulation in 5050:
2020 (20 years) ⇒ 2040 (00 years) ⇒2050= 733,000 + 1,11,000 + 55,500= 8,99,500Therefore, using mathematical operations, the population of Alaska in 2050 will be 8,99,500.
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Answer: 937,723
Step-by-step explanation:
Please help. Albert invested money into the stock market, and the table represents his earnings. What type of function could be used to model his bank account as a function of time? Justify your answer.
Answer:
You have the right answer
Step-by-step explanation:
25.7 cm 6,3 cm 17.3 cm 26.6 cm The perimeter of the figure is on (Type a whole number or a decim ונן"
The perimeter of the figure is 83.2 cm
Here, we want to the perimeter of the figure
To get this, we simply add the lengths of the sides
Mathematically, we have this as;
[tex](7.3+17.3+25.7+6.3+26.6)\text{ cm =83.2 cm}[/tex]Solve for x 5(x - 3) = -11
In order to solve this equation for x, the first step is using the distributive property of multiplication:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]So, solving the equation for x, we have:
[tex]\begin{gathered} 1.\text{ Distributive property on the left side:}\\ \\ 5x-5\cdot3=-11\\ \\ 5x-15=-11\\ \\ 2.\text{ Add 15 to both sides:}\\ \\ 5x-15+15=-11+15\\ \\ 5x=4\\ \\ 3.\text{ Divide both sides by 5:}\\ \\ \frac{5x}{5}=\frac{4}{5}\\ \\ x=\frac{4}{5} \end{gathered}[/tex]Therefore the solution is x = 4/5 or x = 0.8.
The sum of the first five terms of an arithmetic sequence is 20 and the sixth term is 25. What is the first term of the sequence and the common difference?
S5 = 20
A6 = 25
A1=
d=
The general formula for arithmetic sequence is:
An = A1 + (n - 1)d
25 = A1 + 6d - d (1)
And the formula for arithmetic sum:
Sn = n(A1 + An)/2
20 = 5(A1 + 25 - d)/2
8 = A1 + 25 - d (2)
We have a system of two equations with two variables.
25 = A1 + 5d
8 = A1 + 25 - d
For both equations, we can solve for d and then equal both equations as follows:
5 - A1/5 = d (1)
A1 + 17 = d (2)
A1 + 17 = 5 - A1/5
A1 = -10.
Now we just replace the value of A1 in equation 1:
d = 7
Four hundred ninety two in standard form
Answer: 43x10
Step-by-step explanation:
Solve for x: -4x<36
(line underneath the <)
Answer:
Since we are dividing by a negative number, we must reverse the inequality sign.
[tex] - 4x \leqslant 36[/tex]
[tex]x \geqslant - 9[/tex]
Peter is building a fence. If each section is 4 1/2 feet long, how many sections will there be in the finished fence shown?
Using proportions, the number of sections that will be in the finished fence is of:
8.5 sections = 8 and 1/2 (as a mixed number).
What is a proportion?A proportion is a fraction of a total amount, and arithmetic operations such as multiplication or division are used to find the equivalent amounts.
In the context of this problem, we have that the relevant lengths are given as follows:
Each section is of 4.5 feet long.The total length of the fence is of 38.25 feet.Hence, applying a rule of three, as the total length is proportional to the length of each section, the number of sections is given by the division of the total length of the fence by the length of each section, as follows:
Number of sections = 38.25/4.5 = 8.5 sections = 8 and 1/2 (as a mixed number).
What is the missing information?The total length of the fence is missing, and it is of 38.25 feet.
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Graphing Technology RequiredA study investigated the relationship between the amount of daily food waste measured in pounds and the number of people in a household. The data in the table displays the results of the study.Use graphing technology to create the line of best fit for the data in the table.What is the equation of the line of best fit for this data? Round numbers to two decimal places.
In the next graph, the data points and the line of the best fits are shown.
The equation of the line of best fit is:
[tex]y=1.22x-0.09[/tex]
What is 3804 divided by 7?
Answer: 3
Step-by-step explanation:
Multiply the rational expressions and express the product in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(2x^2+9x-35\right)}{\left(x^2+10x+21\right)}\cdot \frac{\left(3x^2+2x-21\right)}{\left(3x^2+14x-49\right)}The numerator is AnswerThe denominator is Answer
Given:
The expression is,
[tex]\frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)}[/tex]Simplify the expression,
[tex]\begin{gathered} \frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)} \\ =\frac{2x^2-5x+14x-35}{x^2+3x+7x+21}\times\frac{3x^2-7x+9x-21}{3x^2-7x+21x-49} \\ =\frac{x(2x^{}-5)+7(2x-5)}{x(x^{}+3)+7(x+3)}\times\frac{x(3x^{}-7)+3(3x-7)}{x(3x^{}-7)+7(3x-7)} \\ =\frac{(2x-5)(x+7)}{(x+3)(x+7)}\times\frac{(3x-7)(x+3)}{(3x-7)(x+7)} \\ \text{Cancel the common factor } \\ =\frac{2x-5}{x+3}\times\frac{x+3}{x+7} \\ =\frac{2x-5}{x+7} \end{gathered}[/tex]Answer:
Numerator is 2x - 5.
Denominator is x + 7.
The diameter of the Sun is 1,400,000 km. The diameter of Earth is 1.28 x10 km. How many times greater is the
diameter of the Sun than the diameter of Earth? Scientific notation
Answer:
[tex]1.09375 \times 10^5[/tex]
Step-by-step explanation:
[tex]1400000=1.4 \times 10^6 \\ \\ \frac{1.4 \times 10^6}{1.28 \times 10}=1.09375 \times 10^5[/tex]
Which of the following events are NOT independent?Select one:A coin is tossed twice in a row.OA red jelly bean is taken from one jar and a yellow jelly bean istaken from another jar.OA card is drawn from a standard deck, and then another cardis drawn without the first one being replaced.A bag contains 2 red marbles, 5 blue marbles, and 3 greenmarbles. A marble is picked and then placed back in the bag.Then another marble is picked.
Solution:
We are required to determine which of the events given in the options are NOT independent?
Note: Not independent in another words means dependent.
Thus, the question is asking us to pick the option that is dependent.
Firstly, let us look at what dependent events are.
Events are dependent if the outcome of one event affects the outcome of another. For example, if you draw two colored balls from a bag and the first ball is not replaced before you draw the second ball then the outcome of the second draw will be affected by the outcome of the first draw.
Now that we understand what dependent events are, let us use that knowledge to select the correct option
(1) A coin is tossed twice in a row.
The outcome of the second throw is not affected by the first throw. Thus, these events are independent
(2) A red jelly bean is taken from one jar and a yellow jelly bean is taken from another jar:
The outcome of the yellow jelly bean taken from one jar is not affected by A red jelly bean is taken from another jar. Thus, these events are independent
(3) A card is drawn from a standard deck, and then another card is drawn without the first one being replaced.
Since the first card drawn is not replaced, the other cards drawn will be dependent on the type of card drawn in the first draw. Thus, these events are dependent
(4) A bag contains 2 red marbles, 5 blue marbles, and 3 green marbles. A marble is picked and then placed back in the bag. Then another marble is picked.
Since the first marble picked is replaced before picking the second one, the second draw will not be affected by the first draw. Hence, these events are independent
Conclusion:
The correct answer is the third option. That is "A card is drawn from a standard deck, and then another card is drawn without the first one being replaced"
Help please show your work please
Therefore Bill will be able to stay 8 days in his vacation.
Given:
Money Bill saved = $3500
Expenditure for plane tickets = $816
Expenditure per day for hotel = $125
Expenditure per day for food = $100
Expenditure per day for sightseeing = $95
Let the no of days Bill can stay be x.
Therefore,
Expenditure for x days for hotel = $125x
Expenditure for x days for food = $100x
Expenditure for x days for sightseeing = $95x
Therefore according to the question:
125x + 100x + 95x + 816 = 3500
=> 320x = 3500 - 816
=>x =8.3
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I would like to know how to solve this & what the answer is?
step 1
Find out the circumference of the circle
[tex]C=Pi*D[/tex]where
D=2(4)=8 km ----> the diameter is two times the radius
substitute
[tex]\begin{gathered} C=pi*8 \\ C=8pi\text{ km} \end{gathered}[/tex]Remember that the circumference subtends a central angle of 360 degrees
so
Applying proportion
Find out the arc length by a central angle of 135 degrees
[tex]\begin{gathered} \frac{8pi}{360^o}=\frac{x}{135^o} \\ \\ x=\frac{8p\imaginaryI}{360^{o}}*135^o \end{gathered}[/tex]x=3pi km
therefore
The answer is 3pi kmGeorge drives a delivery route thatcovers 320 miles each day. He works8 hours each day. How many miles doesGeorge drive each hour?
Gorge drives 40 miles each hour
Explanation:Distance covered per day = 320 miles
Number of hours George works per day = 8 hours
Distance covered by George per hour = 320/8
Distance covered by George per hour = 40 miles
Gorge drives 40 miles each hour
F(x) = x^2 -4x + 6
Find the value of f( - 4)
Write the answer as an integer or a decimal number.
Answer:
38
Step-by-step explanation:
[tex]f(-4)=(-4)^2-4(-4)+6 \\ \\ =16+16+6 \\ \\ =38[/tex]
f(-4) = (-4)^2 -4(-4) +6
f(-4 = 16+16+6
f(-4) = 38)
OGRAPHS AND FUNCTIONSFinding slopes of lines parallel and perpendicular to a line given.
We have the next line:
[tex]-5x\text{ - 7y = -8}[/tex]Solve the equation using the slope-intercept form:
[tex]y\text{ = mx + b}[/tex]Where m is the slope and b is the y-intercept:
Solving the equation:
-5x - y7 = -8
Add 5x on both sides
-5x + 5x - y7 = -8 + 5x
-7y = -8 +5x
Divide by 7 into both sides:
-7y/7 = (-8 +5x)/7
-y = (-8 +5x)/7
Multiply by -1 to calcel the negative sign:
(-1)(-y) =(-1)* (-8 +5x)/7
y = (8 -5x)/7
y = -5x/7 + 8/7
Now, we need to find the slope of a line perendicular to this line.
"Two lines are perpendicular if and only if their slopes are negative" reciprocals"
So the slope, in this case, is -5x/7
To find the perpendicular line use:
-5x/7 * m = -1
Solve the equation m:
m = (-1)/(-5x/7)
m = 7/5x
So m = 7/5x is the slope of the perpendicular line.
To find the parallel line use:
"Two lines are parallel lines if they do not intersect. The slopes of the"
lines are the same."
So m = -5x/7
how to solve 4d without a graphing tool and basically graph the whole equation
The given system of equations is:
[tex]\begin{gathered} x^2+y-3=0 \\ x^2-y+1=0 \end{gathered}[/tex]Add the two equations to eliminate the variable y:
[tex]\begin{gathered} 2x^2-2=0 \\ 2x^2=2 \\ x^2=1 \\ \text{ Therefore,} \\ x=\pm1 \end{gathered}[/tex]Substite x = 1 into the first equation:
[tex]\begin{gathered} (-1)^2+y-3=0 \\ 1+y-3=0 \\ y=3-1=2 \end{gathered}[/tex]Subtitute x=-1 into the second equation:
[tex]\begin{gathered} (1)^2+y-3=0 \\ 1+y-3=0 \\ y=3-1=2 \end{gathered}[/tex]Therefore, the points (-1, 2) and (1, 2) are solutions of the system.
The graph of the system is:
Please help asap due today
Solve y^3 = −125.
y = −5
y = ±5
y = −25
y = ±25
Answer:
A. y = −5
Step-by-step explanation:
Yw :)
