The given expression is :
[tex]\mleft\lbrace x\mright|x\leq-4.3\}[/tex]In the given expression x is less than equal to - 4.3
so, it's domain will lie from - infinity to - 4.3
Thus :
[tex]\text{ Interval Notation: (-}\infty,-4.2\rbrack[/tex]Answer :
[tex]\text{ Interval Notation: (-}\infty,-4.2\rbrack[/tex]apple trees need to be planted in an orchard this process takes two hours per tree
the fact that we can not plant the half of tree imples that there is no line between the points of the graph. So the answer is letter B
a tank in the shape of a sphere is filled with water and has a diameter of 15ft. if water weighs 62.4 pounds per cubic foot what is the total weight of the water in a full tank to the nearest pound
Answer:
110,270 pounds.
Explanation:
Diameter of the Spherical Tank = 15 ft
• Radius = 15 ÷ 2 = 7.5 ft
For any sphere with radius, r:
[tex]\text{Volume}=\frac{4}{3}\pi r^3[/tex]Therefore, the volume of water that will fill the tank:
[tex]\begin{gathered} V=\frac{4}{3}\times\pi\times7.5^3 \\ =1767.15\; ft^3 \end{gathered}[/tex]If water weighs 62.4 pounds per cubic foot:
[tex]\begin{gathered} \text{Density}=\frac{\text{Weight}}{\text{Volume}} \\ 62.4=\frac{\text{Weight}}{1767.15} \\ \text{Weight}=62.4\times1767.15 \\ \text{Weight}=110,270.16\text{ pounds} \\ \text{Weight=}110,270\text{ pounds} \end{gathered}[/tex]The total weight of the water in a full tank is 110,270 pounds. (correct to the nearest pound).
Use the fermi process to estimate the number of bricks needed to fill an empty bathtub assume a typical brick has the length of 4 inches a width of 2 inches and a height of 8 inches a typical bathtub has a length of 60 inches a height of 30 inches and a width of 18 inches
Solution
A brick has the dimension 4in by 2in by 8 in
The bathtub has dimension 60in by 30in by 18in
[tex]\begin{gathered} Volume\text{ of a brick = 4in x 2in x 8in = 64in}^3 \\ Volume\text{ of the bathtub = 60in x 30in x 18in = 32400in}^3 \end{gathered}[/tex]Number of bricks needed to fill an empty bathtub =
[tex]\begin{gathered} \frac{32400in^3}{64in^3}=506.25\text{ bricks} \\ =506\text{ bricks \lparen to nearest whole number\rparen} \end{gathered}[/tex]To
The equation y = 5x represents a proportional relationship. What is the constant of proportionality?A. xB. 1/5C. 0D. 5
ANSWER
D. 5
EXPLANATION
We have to find the constant of proportionality in the equation:
[tex]y=5x[/tex]The general form of a proportional relationship is:
[tex]y=kx[/tex]where k = constant of proportionality
Therefore, comparing the given equation with the general equation, the constant of proportionality is 5.
a cake is in the room, 5he first person takes 1/3 and then the second person takes 1/3 of what is left and so on, c(n) represents the amount of cake left each time find out how much cake there is after 5 people
Let the full cake represent,
[tex]c(1)=1[/tex]Therfore, the given problem is in the form of an arithmetic sequence,
[tex]1,\frac{2}{3},\ldots.[/tex]Here, n=5, d=-1/3, c(1)=1
[tex]c(5)=c(1)+(5-1)\times-\frac{1}{3}[/tex]Therefore,
[tex]\begin{gathered} c(5)=1-\frac{4}{3} \\ =-\frac{1}{3} \end{gathered}[/tex]So, the remaining amount of cake is -1/3.
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 9z
Answer:
(-3, 2)(1, 0)=====================
Given systemy² = 1 - x x + 2y = 1Rearrange the first equationx = 1 - y² Substitute the value of x into second equation1 - y² + 2y = 1y² - 2y = 0y(y - 2) = 0y = 0 and y = 2Find the value of xy = 0 ⇒ x = 1 - 0² = 1y = 2 ⇒ x = 1 - 2² = -3Answer:
[tex](x,y)=\left(\; \boxed{-3,2} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\;\;\;\;\;\;\;y^2=1-x\\x+2y=1\end{cases}[/tex]
To solve by the method of substitution, rearrange the second equation to make x the subject:
[tex]\implies x=1-2y[/tex]
Substitute the found expression for x into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}x=1-2y \implies y^2&=1-(1-2y)\\y^2&=1-1+2y\\y^2&=2y\\y^2-2y&=0\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}\implies y^2-2y&=0\\y(y-2)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for y:
[tex]\implies y=0[/tex]
[tex]\implies y-2=0 \implies y=2[/tex]
Substitute the found values of y into the second equation and solve for x:
[tex]\begin{aligned}y=0 \implies x+2(0)&=1\\x&=1\end{aligned}[/tex]
[tex]\begin{aligned}y=2 \implies x+2(2)&=1\\x+4&=1\\x&=-3\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-3,2} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{1,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
The population of a city was 136 thousand in 1992. The exponential growth rate was 1.7% per year.a) Find the exponential growth function in terms of t, where t is the number of years since 1992.P(t) = 136,000 e 0.0177
We will have that the expression will be:
[tex]p(t)=136000(1+0.017)^t[/tex]Help Curtis round 37,254,503 to the nearest hundred thousand for his report.
the answer is:
37, 300, 000
Answer:
37,300,500
Step-by-step explanation:
Can you please help me with number 34. Determine the number of ways that each can occur
You need to determine the number of possible combinations when you choose 4 appetizers out of 11 options in the dinner menu. Assuming that you are not going to repeat appetizers, to determine this number you have to apply combinations, using the formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]Where
n is the number of options available
r is the number of options you have to choose, with no repetition, and the order doesn't matter.
For this exercise:
n=11
r=4
The combination can be determined as follows:
[tex]\begin{gathered} C(11,4)=\frac{11!}{4!(11-4)!} \\ C(11,4)=\frac{11!}{4!\cdot7!} \\ C(11,4)=\frac{39916800}{24\cdot5040} \\ C(11,4)=330 \end{gathered}[/tex]There are 330 combinations possible to choose 4 out of 11 appetizers from the menu.
Robert moved 4 cards that are worth -10 points each. How did thier score change.
We have the following:
Since there are 4 cards and each one has a value of -10 points, we have
[tex]4\cdot-10=-40[/tex]Which means that the score changed by -40 points
A recipe calls for 1/2 cup sugar, a cup of flour and 1/3 cup of milk. I need to make 3 batches. How much of each ingredient will I need?
The recipe calls for
1/2 cup of sugar : 1 cup of flour : 1/3 cup of milk for 1 batche
We need to make 3 batches, so
Multiply each ingredient bu 3
Sugar = 1/2 * 3 = 3/2 cups
Flour = 1 * 3 = 3 cups
Milk = 1/3 * 3 = 1 cup
3/2 cups of sugar : 3 cups of flour : 1 cup of milk
find the correct area
The figure consist of trapezium and rectangle.
Determine the area of figure.
[tex]\begin{gathered} A=\frac{13+24}{2}\cdot4+24\cdot7 \\ =37\cdot2+168 \\ =74+168 \\ =242 \end{gathered}[/tex]Thus area of the figure is 242 inch square.
2x - 1 if x < 0Evaluate g (4) for g(x)for g(x) = x²W√xif 0 ≤ x ≤ 5.if x > 5
Solution
Question A:
[tex]\begin{gathered} \text{ To find the rate we compare with the equation below:} \\ A=P(1+r)^t \\ \\ \text{ Thus, } \\ 1+r=0.9 \\ \text{ Subtract 1 from both sides} \\ r=0.9-1 \\ r=-0.1 \end{gathered}[/tex]- Rate of depreciation is 10%
Question B:
[tex]\begin{gathered} v=34000(0.9)^t \\ \text{ when } \\ v=\frac{34000}{2}=17000 \\ \\ 17000=34000(0.9)^t \\ \text{ Divide both sides by 34000} \\ 0.5=(0.9)^t \\ \text{ Take the natural log of both sides} \\ \ln0.5=t\ln0.9 \\ \\ \therefore t=\frac{\ln0.5}{\ln0.9} \\ \\ t=6.578813...\approx6.58years \end{gathered}[/tex]- The number of years is 6.58years
The highest recorded temperature in Massachusetts was one hundred seven degrees Fahrenheit on August 27, 1975. The average monthly high temperature is 81.7 degrees Fahrenheit. How many degrees hotter than average was the temperature on August 27, 1975?
Answer:
25.3°F
Explanation:
We need to find the difference between the temperature on August 27, 1975, and the average temperature. So, the difference is equal to:
107 °F - 81.7°F = 25.3°F
It means that on August 27, 1975, the temperature was 25.3°F hotter than average.
how would you write this as an expression.
The quotient of 29 and the product of a number and −5.
ANSWER
[tex]\frac{29}{-5x}[/tex]EXPLANATION
Let 'x' be a number. The product of a number and -5 is: -5x
Then the quotient of 29 and something is: 29/something
Now, that something is the product -5x so, the quotient of 29 and the product of a number and -5 is:
[tex]\frac{29}{-5x}[/tex]Grayson needs to order some new supplies for the restaurant where he works. The restaurant needs at least 261 forks. There are currently 205 forks. If each set on sale contains 10 forks, which inequality can be used to determine the minimum number of sets of forks Grayson should buy?
ANSWER
[tex]10x\ge56[/tex]EXPLANATION
We have that the restaurant needs at least 261 forks.
There are currently 205 forks.
First, we have to find the number of forks that the restaurant currently needs.
We do that by finding the difference between the number of forks they have from the number of forks they need:
261 - 205 = 56 forks
They need at least 56 forks.
We have that each set of forks on sale has 10 forks each.
Let the number of sets they need be x.
This means that the amount of forks they should buy must be greater than or equal to 56. That is:
[tex]\begin{gathered} x\cdot10\ge56 \\ \Rightarrow10x\ge56 \end{gathered}[/tex]That is the inequality that can be used to determine the minimum number of sets of forks Grayson should buy.
which choice is equivalent to the fraction below? hint: rationalize the denominator and simplify. 6 over the square root of 2.
Answer
(6/√2) = 3√2
Explanation
We are asked to simplify
6/√2
So, we will rationalize this by multiplying numerator and denominator by √2
[tex]\frac{6}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{6\sqrt[]{2}}{\sqrt[]{2}\times\sqrt[]{2}}=\frac{6\sqrt[]{2}}{2}=3\sqrt[]{2}[/tex]Hope this Helps!!!
The plastic lid of a cylindrical container is a circle. The lid has a radius of 9centimeters. What is the circumference of the lid?
We are asked to determine the circumference of a 9 cm radius circle. To do that we will use the following formula:
[tex]S=2\pi r[/tex]Where:
[tex]\begin{gathered} S=\text{ circumference} \\ r=\text{ radius} \end{gathered}[/tex]Now, we substitute the value of the radius:
[tex]S=2\pi(9cm)[/tex]Solving the operations:
[tex]S=18\pi=56.55cm[/tex]Therefore, the circumference is 56.55 cm.
Deon had $25 then he spent $15 on lunch. What percentage of his money did deon spend on lunch
Initial amount = $25
Amount spent on lunch = $15
The percentage of money spent on lunch
[tex]\frac{Amount\text{ spent}}{Initial\text{ amount}}\text{ x 100\%}[/tex][tex]\frac{15}{25}\text{ x 100 \%}[/tex][tex]\begin{gathered} \frac{1500}{25}^{} \\ =\text{ 60\%} \end{gathered}[/tex]The list price for a case of medicine is $275.49 Your pharmacy will receive a 18% trade discount. What is the amount of the discount? b) What is the net cost of the case of medicine?
The amount of the discount is $49.59, and the net cost after the discount is applied is $225.90.
What is the amount of the discount?If we have a original price P and we apply a discount of X, where X is a percentage, the amount of the discount is given by the formula:
D = P*(X/100%)
In this case, the original price is $275.49 and the discount is of 18%, then the amount of the discount is:
D = $275.49*(18%/100%) = $275.49*0.18 = $49.59
b) To get the net cost we need to take the difference between the original price and the amount of the discount, we will get:
net cost = $275.49 - $49.59 = $225.90
Learn more about discounts:
https://brainly.com/question/7459025
#SPJ1
Topic 4,: Graphing Proportional relationships.Note: A way to determine whether two quantities are proportional is to graph themon a coordinate plane. If the graph is a straight line through the origin, then the twoquanti1lies are proportional.Ex 4. Determine whether the number of calories burned is proportional to thenumber of minutes played
Given
Table:
Time: 0, 1, 2, 3, 4
Calories: 0, 7, 14, 21, 28
Procedure
Let's plot the points shown
We can see that the points fall on a straight line. Therefore time and calories are two proportional quantities.
What numeric value of b would make the following two expressions equivalent? bx +2.4 and 6(2x+0.4) + 3x
For the two expressions to be equivalent, then we would have;
[tex]bx+2.4=6(2x+0.4)+3x[/tex]We solve the right hand side and we'll now have;
[tex]\begin{gathered} bx+2.4=12x+2.4+3x \\ bx+2.4=15x+2.4 \\ \text{Collect all like terms and you'll have} \\ 2.4-2.4=15x-bx \\ 0=15x-bx \\ Add\text{ bx to both sides of the equation} \\ 0+bx=15x-bx+bx \\ bx=15x \\ \text{Divide both sides by x} \\ \frac{bx}{x}=\frac{15x}{x} \\ b=15 \end{gathered}[/tex]The first option is the correct one.
b = 15
Your lacrosse team wins 4 of the games that it plays. Describe huikelihood of winning.
the statement say us the rate of winning is 3/4 then the probability is the same
but performance it on decimals
[tex]\frac{3}{4}=0.75[/tex]probability is 0.75
Three values on a number line ate labeled f, g and h.
• f = -4
,• g = -g
,• h = -f
ExplanationLet us find the values of g and h.
• Since we know the value of, we can find the value of h.
[tex]\begin{gathered} h=-f \\ h=-(-4) \\ h=4 \end{gathered}[/tex]• We solve the given equation for g.
[tex]\begin{gathered} g=-g \\ \text{ Add g from both sides} \\ g+g=-g+g \\ 2g=0 \\ \text{ Divide by 2 from both sides} \\ \frac{2g}{2}=\frac{0}{2} \\ g=0 \end{gathered}[/tex]AnswerTherefore, the number line that shows correctly the values of f,g, and h is the one in option c.
how would you graph a figure that is translated by (x-4, y+2
AC=AB=16cm.BC=20cm. How do i find the height of the triangle?
Given that
[tex]\begin{gathered} AB=AC=16\operatorname{cm} \\ BC=20\operatorname{cm} \\ BD=\frac{BC}{2}=\frac{20\operatorname{cm}}{2}=10\operatorname{cm} \\ CD=\frac{BC}{2}=\frac{20\operatorname{cm}}{2}=10\operatorname{cm} \\ AD=h \end{gathered}[/tex]To calculate the height of the triangle, we will use the Pythagoras theorem
With the Pythagorean theorem, we will have
[tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{where,} \\ \text{HYPOTENUS}=AC=16\operatorname{cm} \\ \text{opposite}=DC=10\operatorname{cm} \\ \text{adjacent}=AD=h \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ 16^2=10^2+h^2 \\ 256=100+h^2 \\ \text{substract 100 from both sides} \\ 256-100=100-100+h^2 \\ 156=h^2 \\ \text{square root both sides} \\ \sqrt[]{h^2}=\sqrt[]{156} \\ h=\sqrt[]{4}\times\sqrt[]{39} \\ h=2\sqrt[]{39} \\ or\text{ } \\ h=12.39\operatorname{cm}\approx to\text{ 1 d.p=} \\ h=12.5\operatorname{cm} \end{gathered}[/tex]Therefore,
The height of the triangle is = 12.5 cm
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Whats the other side?
Image attached
please show work
The perimeter of the rectangle is 129.2×10⁵ if the area and one side of the rectangle is given.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
It is given that:
The area of the rectangle = 2.76×10¹² square cm
The length of the rectangle = 4.6×10⁵ cm
The other side measure = 2.76×10¹²/4.6×10⁵ = 0.6×10⁷ = 60×10⁵ cm
The perimeter of the rectangle = 2(4.6×10⁵ + 60×10⁵)
The perimeter of the rectangle = 129.2×10⁵
Thus, the perimeter of the rectangle is 129.2×10⁵ if the area and one side of the rectangle is given.
Learn more about the rectangle here:
https://brainly.com/question/15019502
#SPJ1
What number makes the equation true? Enter the answer in the box.+5= 9
The complete information for the question was not provided by the student, however we can assume that the box is either to the left or to the right of the equal sign:
If it's to the left, we have:
Box + 5 = 9
Box = 9 - 5
Box = 4
If it's to the right, we have:
5 = 9 - Box
5 - 9 = - Box
-4 = - Box
4 = Box
Answer: No matter if the box is to the left or to the right of the equal sign, the number in the box that makes the equation true is 4
is( 1,9)a solution to the equation y=x
is( 1,9) a solution to the equation y=x
answer is
is not a solutionbecause y=x means
the value of x is equal to the value of y
and 1 is not equal to 9