The length of the straw is equal to the length of the space diagonal of rectangular box, that is 11.6 inches.
The length of the straw is equal to the space diagonal of the rectangular box. Space diagonals are three-dimensional diagonals.
If the length of the sides of the box is a, b, and c, then the space diagonal can be computed by applying the Pythagorean Theorem.
D = √(a² + b² + c²)
Substitute the following dimensions:
a = 10 inches
b = 3 inches
c = 5 inches
Then,
D = √(10² + 3² + 5²)
D = √(100 + 9 + 25)
D = √134 = 11.6 inches
Hence, the length of the straw is 11.6 inches.
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Write the word sentence as an equation. Then solve the equation.
9 is the difference of a number n and 7.
An equation that represents this word sentence is
The solution is n=
The equation that represents this word sentence is n-7 = 9
The value of n = 16
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of variables, terms, coefficients, constants and factors.
They are also made up of mathematical or sometimes called arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFloor divisionFrom the information given, we have that;
9 is the difference of a number n and 7.
This is represented as;
n - 7 = 9
Now, collect like terms
n = 9 + 7
Add the values
n = 16
Thus, the value is 16
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In the figure, point $A$ is the center of the circle, the measure of angle $RAS$ is 74 degrees, and the measure of angle $RTB$ is 28 degrees. What is the measure of minor arc $BR$, in degrees
In circle A, angle RAS is 74 degrees and angle RTB is 28 degrees. The measure of minor arc BR is 81 degrees.
The figure is in the attached picture.
Notice that:
AS = AR = radii of the circle.
Hence, triangle SAR is an isosceles triangle, and ∠ASR = ∠ARS.
The sum of angles in a triangle is 180°.
Therefore,
∠ARS + ∠ASR+ 74° = 180°
Since ∠ASR = ∠ARS,
2∠ARS + 74° = 180°
2∠ARS = 106°
∠ARS = 53°
and
∠ASR = ∠ARS = 53°
Angle in a straight line:
∠AST + ∠ASR = 180°
∠AST = 180° - ∠ASR = 180° - 53° = 127°
Refer to triangle SAT:
∠SAT = 180° - 28° - 127° = 25°
The measure of minor arc BR = ∠RAB
∠RAB = 180° - 74° - 25°
∠RAB = 81°
The picture in your question is missing, but most likely it was in the attached picture.
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ace pharmaceutical has developed a drug that it believes will help lower cholesterol and blood pressure at a significantly greater rate than fish oil. researchers wish to test the new drug and compare the results to those of fish oil and of a placebo. a total of 300 volunteers suffering from hypertension and high cholesterol will participate in the study. part a explain how you would carry out this test in a completely randomized experiment.
The subjects would be randomized at random to receive the new medication, fish oil, or a placebo. The effectiveness of the new variance medicine would next be evaluated by comparing the outcomes of the various therapies.
The test would be conducted using a completely randomized experiment. This means that the 300 volunteers would be randomly assigned to the three different treatments: the new drug, fish oil, or the placebo. This ensures that any differences between the groups can be attributed to the treatments, and not any other factor. The volunteers would be monitored for a period of time, and the results of the treatments would be compared to determine the effectiveness of the new drug. This could be done through measuring changes in cholesterol and blood pressure levels, as well as any side effects of the treatments. In addition, the volunteers’ health and dietary habits should be monitored to ensure that any differences between the treatments are not caused by any other factors.
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Please it’s a simple maths question :)
Answer:
1. To find the gradient of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.
a) To find the gradient of (x+7)/(y-2) = 0, we can first rewrite the equation as y = (2x+14)/(x+7). To find the slope, we can take the derivative of y with respect to x. We get the slope or the gradient of the line as m = 2/(x+7).
b) To find the gradient of the line through (p,5) and (6,2p), we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and solve for m.
y - 5 = m(x - p)
2p - 5 = m(6 - p)
2p - 5 = 6m - mp
mp + 6m = 2p + 5
m(p+6) = 2p + 5
m = (2p+5)/(p+6)
2. To find the equation of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.
a) To find the equation of the line with a gradient of 3, passing through (0,5), we can substitute the values into the slope-intercept form.
y = 3x + b
5 = 3(0) + b
b = 5
The equation of the line is y = 3x + 5
3. To find the value of p, if the gradient of the line joining (-1,p) and (p, 4) is 2/3, we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and the gradient, and solve for p.
y - p = (2/3)(x - (-1))
4 - p = (2/3)(p - (-1))
4 - p = (2/3)p + (2/3)
(2/3)p - 4 + p = (2/3)
p = 6
Final Answer: The value of p is 6.
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=88(0.977)^x
3% is the percentage rate of increase or decrease.
What does exponential decay mean?
A process known as exponential decay describes how a quantity depletes over time, with the rate of depletion become proportionately slower as the quantity shrinks. Finding the exponential drop—a rapid reduction over time—is made easier by the exponential decay formula.
The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay. The formula for f(x) is f(x) = a (1 - r)x.
The formula for exponential decay is y=a(1-r)x.
r is the decay rate, expressed as a decimal.
In this case, r = .03 which represents 3%
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1. a woodworker produces 2 chairs every day. the company that buys the chairs randomly selects the days on which to check the chairs made that day. does this result in a random sampling? yes, because each item has an equal chance of being selected. no, because each group of n items does not have an equal chance of being selected. yes, because each group of n items has an equal chance of being selected. no, because each item does not have an equal chance of being selected.
Yes, this results in a random sampling because every day the woodworker produces two chairs, and the company that buys the chairs randomly selects the days on which to check the chairs made that day.
This means that each item (each chair) has an equal chance of being selected, and each group of n items (in this case, two chairs) also has an equal chance of being selected. The probability of an item being selected can be calculated using the formula P(A) = n/N, where n is the number of items in the sample and N is the total number of items in the population. In this case, the probability of an item being selected is 2/2 = 1, and the probability of a group of two items being selected is 2/2 = 1. This shows that each item and each group of items has an equal chance of being selected, which means that this is a random sampling.
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Which scenario does NOT represent an additive relationship? A) Mason is five years older than Greg. B) Apples cost $2.50 per pound. C) Bernie's Burgers charges a $3.00 delivery fee for all orders. D) Perla's Pet Shop is offering a $5.00 coupon off any order.
Answer:
B. Apples cost $2.50/pound
Step-by-step explanation:
B would be a multiplicative relationship because you would multiply the number of pounds by 2.50
Use the graphs to evaluate the expressions below.
Answer:
[tex]f(g(4) = \boxed{\bold{0}}[/tex]
[tex]g(f(3)) = \boxed{\bold{2}}[/tex]
[tex]f(f(5)) = \boxed{\bold{5}}[/tex]
[tex]g(g(1)) = \boxed{\bold{4}}[/tex]
Step-by-step explanation:
All the expressions are composite functions where the output of one function is fed as input to the other function to get the composite output
To explain better, I will use the specific values and the graphs of f(x) and g(x)
-----------------------------------------------------------------------------------------------------
f(g(4))
Let's take the first expression [tex]\displaystyle {f(g(4))}[/tex]. The innermost function, [tex]g(x)[/tex] is first evaluated at [tex]x = 4[/tex], then this value is used to find the value of the outer function [tex]f(x)[/tex]
To find the value of this expression
Look at the [tex]g(x)[/tex] graph on the right, find out the value for g(4). On this graph we see that when x = 4, [tex]g(x)[/tex] is 3.-----------------------------------------------------------------------------------------------------
The other expressions can be evaluated using similar reasoning.
g(f(3))
First evaluate[tex]f(x) \:at\: x = 3 == > f(3) = 0 == > g(0) = 2[/tex]
Answer: 2
-----------------------------------------------------------------------------------------------------
f(f(5))
This is a function which is a composite of itself
Find [tex]f(5) = 2 == > f(2) = 5[/tex]
Answer: 5
-----------------------------------------------------------------------------------------------------
g(g(1))
[tex]g(1) = 5 == > g(5) = 4[/tex]
Answer: 4
19>15+x I am so confused and need help for homework.
Answer: x<4
Step-by-step explanation:
19>15+x
4>x
x<4 is the answer
Answer:
Since 15+x is less than 19. 15+x cannot equal to or greater than 19. If x is greater or equal to 4, the answer will be equal to or greater than 19 which is not true for the equation shown above.
So x is less than 4.
I need help with division 3,340 divided by 8
Answer: 42.5
Step-by-step explanation:
8 multipled by 42.5 is 340. A strategy i use is multiply 8 by 5 or 10, for example 8 times 5 is 40, so i know that 8 times 50 is 400, that tells you the answer you need is just a little below 50
The list shows numbers in order from least to greatest. -15, -3 4/5, -1.5, ____, 2.3, 5 2/3Which is an integer that can be inserted on the blank line in the list?a.-2 b. -1 1/3 c. 0 d. 1.2
An integer that can be inserted on the blank line in the list from the given options is 0.
Therefore the answer is c) 0.
The list shows numbers in order from least to greatest, that is ascending order -15, -3 4/5, -1.5, ____, 2.3, 5 2/3
The integer that can be inserted on the blank line in the list is c. 0, because it is greater than -1.5 and less than 2.3 and it is an integer.
-2 is less than -1.5. So they cannot be the answer. -1 1/3 is equal to -4/3 and 1.2 is greater than -1.5 and less than 2.3, but they are not integers.
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Write an equation of the line passing through the point (8, 7) that is perpendicular to the line y 7
The equation of the line would be y = 17/7x + 1.
What is the equation of the line?
The equation of a line is a mathematical expression that describes the position of a line in a coordinate plane. It typically takes the form of "y = mx + b", where "m" is the slope of the line and "b" is the y-intercept, the point where the line crosses the y-axis.
The whole question is:
Write an equation of the line passing through the point (8,7) that is perpendicular to the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex]
To write the equation of a line that is perpendicular to a given line, we can use the slope of the given line and the point the new line passes through.
The slope of the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] can be found by isolating y and then taking the derivative, which gives us: -7/17.
The slope of a line perpendicular to this line is the negative reciprocal of the given line's slope, which is 17/7.
We also know that the new line passes through the point (8,7). Using a point-slope form of a line which is (y-y1) = m(x-x1) where m is the slope, we can write the equation of the line as:
y - 7 = 17/7(x - 8)
So the equation of the line that passes through the point (8,7) and is perpendicular to the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] is:
y = 17/7x + 1
Hence, the equation of the line would be y = 17/7x + 1.
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Find the area of the following figure. Pictures are not drawn to scale. Round answers to the nearest tenth.
The area of the trapezium is 36.3 unit squared.
How to find area of a figure?The figure above is a trapezium. Therefore, the area of a trapezium can be represented as follows:
Hence,
area of a trapezium = 1 / 2 (a + b)h
where
h = heighta and b are the top and base of the trapeziumTherefore,
area of a trapezium = 1 / 2 (a + b)h
where
a = 4b = 7 + 1.5 = 8.5Using Pythagoras's theorem,
c² = a² + b²
where
a and b are the legsc is the hypotenuseh² = 6² - 1.5²
h²= 36 - 2.25
h = √33.75
h = 5.80947501931
h = 5.81
Therefore,
area of the trapezium = 1 / 2 (4 + 8.5)5.8
area of the trapezium = 1 / 2 (12.5)5.8
area of the trapezium = 72.5 / 2
area of the trapezium = 36.3 units²
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The coefficient of x^7 in the expression (x^3+4/x^2)^4 is
The coefficient of x⁷ in the given expression is 16.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given is the expression [x³ + (4 / x²)]⁴.
[x³ + (4 / x²)]⁴ = (x³ + 4x⁻²)⁴
= (x³ + 4x⁻²)² (x³ + 4x⁻²)²
= (x⁶ + 8x + 16x⁻⁴) (x⁶ + 8x + 16x⁻⁴)
= x¹² + 8x⁷ + 16x² + 8x⁷ + 64x² + 128x⁻³ + 16x² + 128x⁻³ +
256x⁻⁸
Rearranging with like terms, we get,
= x¹² + 16x⁷ + 96x² + 256x⁻³ + 256x⁻⁸
Hence the coefficient of x⁷ is 16.
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◄) A large square is composed of 16 smaller squares that are all the same size. Each of the small squares has an area of 4 square units. What is the side length of the large square?
Answer:
8
Step-by-step explanation:
Each of the small squares has an area of 4 square units
so its length is 2 because 2*2 =4
so 4 small squares = 8 each side
The following equation is being multiplied by the LCD. Complete the multiplication to eliminate the denominators
x+2/3x - 1/x-2 = x-3/3x
(3x)(x-2) [x+2/3x - 1/x-2] = (3x)(x-2) [x-3/3x]
The resulting equation is ___
The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).
The lowest integer that unites all of the fractions in a given collection is known as the least common denominator (LCD).
Given that,
The equation x+2/3x - 1/x-2 = x-3/3x is being multiplied by the least common denominator (LCD)
So, further solving this equation,
x+2 / 3x - 1/x-2 = x-3/3x
Here, the least common denominator (LCD) is (3x)(x-2). so we multiply the whole equation by the least common denominator (LCD).
(3x)(x-2) (x+2/3x - 1/(x-2) = x-3 / 3x)
We multiply each term by the least common denominator (LCD).
(3x)(x-2) (x+2/3x) - (3x)(x-2)(1/(x-2)) = (3x)(x-2)(x-3 / 3x)
Thus, we get (x-2) (x+2)-1(3x) = (x-3) (x-2).
Therefore,The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).
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Answer:
D
Step-by-step explanation: answer is d
a triangular parcel of land has 114 meters of frontage, and the other boundaries have lengths of 70 meters and 95 meters. what angles does the frontage make with the two other boundaries? (round your answers to one decimal place.)
Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.
What is triangle ?
A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always equals 180 degrees. Triangles can be classified based on the length of their sides or the measure of their angles.
We can use the law of cosines to find the angles. The law of cosines states that for any triangle, the square of one side length is equal to the sum of the squares of the other two side lengths, minus twice the product of the other two side lengths multiplied by the cosine of the angle opposite the first side.
Let A, B, and C be the angles opposite the sides of length 114 meters, 70 meters, and 95 meters, respectively.
We can use the following equation to find angle A:
cos A = (70^2 + 95^2 - 114^2) / (2 * 70 * 95)
Once we have the value of cos A, we can use the inverse cosine function to find the angle A in degrees.
Similarly, we can use the same formula to find the angle B and C.
cos B = (114^2 + 95^2 - 70^2) / (2 * 114 * 95)
cos C = (114^2 + 70^2 - 95^2) / (2 * 114 * 70)
Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.
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two ice cream machines make a total of 320 gallons in a certain amount of time. working together for the same length of time, how many gallons of ice cream can each number of machines make? 3 ice cream machines
3 ice cream machines will make a total of 480 gallons for the same length of time and 4 ice cream machines will make a total of 640 gallons for the same length of time.
For the quantity 3 ice cream machines will make.
2 ice cream machines produce a total of 320 gallons in a certain amount of time.
If 2 ice cream machines can make a total of 320 gallons. Then,
3 ice cream machines will produce a total of x gallons in the same amount of time
x = (320 × 3)/2
x = 480 gallons
Hence, 3 ice cream machines will produce a total of 480 gallons.
For the quantity 4 ice cream machines will make.
If 2 ice cream machines can make a total of 320 gallons. Then,
4 ice cream machines will produce a total of y gallons in the same amount of time
y = (320 × 4)/2
y = 640 gallons
Hence, 4 ice cream machines will produce a total of 640 gallons.
--The given question is incomplete, the complete question is
"Two ice cream machines make a total of 320 gallons in a certain amount of time. Working together for the same length of time, how many gallons of ice cream can each number of machines make?
3 ice cream machines
4 ice cream machines"--
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What is formula data type?
Formula data type is used to determine different values based on a variety of fields in the existing table.
It also helps to create a pattern that takes input from all the fields and gives you the final value. Other fields include constants or functions and by using formula data type, you can remove the need to repeatedly enter the same information again and again. It also eliminated the margin of error that could occur during manual entry in the entirety of your work. Formula data type is used to help solve a combination of different equations that have different fields and/or equations.
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the backyard if a new home is shaped like a trapezoid with a height of 40 ft and bases of 73 ft and 111 ft. what is the cost of putting sod on the gard, if the landscaper charge 23 cent per square foot for sod
The cost of putting sod on the gard, given the area of the trapezoid backyard of the new home, is $ 864 . 40
How to find the area of a trapezoid ?The backyard of the new home is said to be shaped like a trapezoid which means that the cost of putting sod on the gard can be found by checking for the area of the trapezoid.
The area of a trapezoid can be found by the formula :
= (( Base A + Base B ) x height ) / 2
= ( ( 73 + 111 ) x 40 ) / 2
= 3, 680 square feet
The cost of putting sod on the gard is therefore:
= Area of the backyard x cost per square foot of sod
= 3, 680 x 0. 23
= $ 864 . 40
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Can anyone help me with this question?
Answer:
A. Yes, opposite sides are congruent.
Step-by-step explanation:
For B, you can't necessarily tell if they are right angles because there is nothing indicating that it is. For C, just because angle measures aren't given doesn't mean that they aren't congruent. For D, sure it could be a rhombus although it doesn't look like it but rhombuses' are parallelograms.
Which value could be substituted for the variable to make the equation
TRUE? w-11 =15
Answer:
26 - 11 = 15
Step-by-step explanation:
First Bank Credit Card
- No interest for 6 months. < $1000
- $10 fee per year
Will wants to buy a new TV for $900. What is the minimum payment that she must pay each month to avoid paying interest on her credit card?
(please answer jojosiwa needs help)
The minimum monthly payment so that she avoids paying interest on the credit card is given as follows:
$150
How to obtain the minimum monthly payment?The minimum monthly payment is obtained applying the proportions in the context of this problem.
The interest-free period is given as follows:
6 months, as long as the purchase has a value that is less than $1000.
(as stated in the problem).
The value of the TV is given as follows:
$900.
(as stated in the problem).
The minimum monthly payment is obtained with the division of the value of the TV by the length in months of the interest free period, as follows:
Minimum payment = 900/6
Minimum payment = $150.
(this is the proportion that is applied in this problem).
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The mean of a set of data is 4.11 and its standard deviation is 3.03. Find the z score for a value of 10.86.
If the mean of a set of data is 4.11 and its standard deviation is 3.03. the z score for a value of 10.86 is: 2.23.
How to find the z-score?Using this formula to find the z-score
z-score = Value - Mean / Standard deviation
Where:
Value = 10.86
Mean = 4.11
Standard deviation = 3.03
Let plug in the formula
z-score = 10. 86 - 4.11 / 3.03
z-score = 6.75 /3.03
z-score = 2.227
z- score = 2.23
Therefore the z-score is 2.23.
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Which algebraic expression is equivalent to 9(4x + 8) - 4
Answer: 36x + 68
Step-by-step explanation:
Expanding it, you get:
36x + 72 - 4
= 36x + 68
PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!
A figure is transformed according to the rule (x,y)= (x-1,y+4). Describe exactly what type of transformation has taken place.
Answer:
The transformation described is a horizontal translation of 1 unit to the left and a vertical translation of 4 units up. The transformation moves every point on the x-axis one unit to the left and every point on the y-axis four units up.
Step-by-step explanation:
It can also be thought of as a transformation that shifts the entire figure one unit to the left and four units up.
A craft store buys 150 feet of satin ribbon for $13.50. The store sells the ribbon by the foot. A customer can purchase 5 feet of ribbon for $0.80. How much profit does the craft store earn on each foot of ribbon?
The profit per foot of the satin ribbon that the craft store buys and sells is $0.80.
How is the profit determined?The profit generated by the craft store per foot is determined by reducing the transactions to their unit cost and price.
The profit per unit becomes the difference between the unit selling price and the unit cost.
In other words, the profit per unit is the unit rate (per-unit profit) or ratio obtained as a difference between two unit parameters.
The cost of buying 150 feet of satin ribbon = $13.50
The unit cost per foot = $0.09 ($13.50/150)
The sales price for 5 feet = $0.80
The unit selling price per foot = $0.16 ($0.80/5)
The profit per unit = $0.80 ($0.16 - $0.80)
Profit percentage = 100% ($0.80/$0.80 x 100)
Thus, we can conclude that the craft store generates a 100% profit or $0.80 per foot.
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you have a fair coin and want to calculate the probability that if you flip the coin 20 times, you will get exactly 14 heads. what is the probability for this event?
The probability of getting exactly 14 heads by flipping a fair coin 20 times is 0.03696.
The number of times a fair coin is flipped = 20
The outcomes for flipping the coin once = 2
Therefore, the outcomes for flipping the coin 20 times = (2) ^ 20
Number of heads needed = 14
The number of ways of getting exactly 14 heads = 20C14
20C14 is the 20! / (14! (20-14)! = 38760
Probability of getting an event = possible outcome / total outcomes
Thus, the probability of getting exactly 14 heads by flipping a fair coin 20 times = (20C14) / (2 ^ 20) ≈ 0.03696
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a bag contains ten balls, some of which are red and the rest of which are yellow. when two balls are drawn at random at the same time, the probability that both balls are red is $\frac{1}{15}$. how many balls in the bag are red?
On solving the provided question we can say that Probability of Red * Second Draw Probability of Red = [tex]3 / 10 * 2 / 9 = 6 / 90 = 1 / 15[/tex]
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
Let the number of red balls = x
[tex][x / 10] * [ (x - 1) / 9 ] = 1/15 \\x(x - 1) / 90 = 1/15 \\x ( x - 1) = 6 \\x^2 - x - 6 = 0 \\(x -3) ( x + 2) = 0 \\x = 3 or x = -2[/tex]
here are 3 red balls
Probability of Red * Second Draw Probability of Red
[tex]3 / 10 * 2 / 9 = 6 / 90 = 1 / 15[/tex]
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3/5 + 5/7 = ____
6/12 + 9/12 ____
1/4 + 4/4 = ____
2/3 + 5/3 = ____
(fractions)
Answer:
1. 46/35 or 1 11/35
2. 5/4 or 1 1/4
3. 5/4 or 1 1/4
4. 7/3 or 2 1/3
Step-by-step explanation:
