suppose you have a 100 millimeter cup a 300 millimeter cup and a 500-milliliter cup list two different ways you can measure exactly 1 liter
What is the length of the altitude of the equilateral triangle below?
the actual right answer is c.
ANSWER
The length of the altitude is [tex]3\sqrt{3}[/tex] units
EXPLANATION
The altitude of a triangle is the vertical height of the triangle.
From the diagram the altitude is [tex]a[/tex]
Method 1: We can use Pythagoras theorem to find [tex]a[/tex]
[tex]6^2=a^2+3^2[/tex]
[tex]6^2-3^2=a^2[/tex]
[tex]36-9=a^2[/tex]
[tex]27=a^2[/tex]
We take the square root of both sides,
[tex]\sqrt{27}=a[/tex]
[tex]\sqrt{9\times3}=a[/tex]
[tex]\sqrt{9} \times \sqrt{3}=a[/tex]
[tex]3\sqrt{3}=a[/tex]
Method 2 Using Trigonometry
[tex]sin(60\degree)=\frac{a}{6}[/tex]
[tex]6sin(60\degree)=a[/tex]
[tex]a=6\times \frac{\sqrt{3}} {2}[/tex]
[tex]a=3\sqrt{3}[/tex]
the map shown is scale of 1:50 000
1) measure and state in centimeters the distance on the map from L to M
2) Calculate the actual distance in kilometers from L to M
3) The actual distance two points is 4.5 km calculate the number of centimeters that should be used to represent the distance one the map
The measure of L to M on the map is 5.8 cm . The actual distance in kilometers is 2.9km and the drawing distance corresponding to 4.5km is 9 cm.
1.)
The distance between points L and M in the drawing is 5.8 cm
2.)
Using the scale given
1 : 500001cm on the map represents 50,000 cm on ground
1 cm = 50000
5.8 cm = x cm
x = 5.8 × 50000
x = 290000 cm
converting to kilometers:
100000 cm = 1 km
290000/100000
= 2.9 km
Hence, the distance in kilometers is 2.9 km.
3.)
Given an actual distance of 4.5 km
4.5 km = 450000 cm
1 cm = 50000 cm
x cm = 450000
50000x = 450000
x = 450000/50000
x = 9 cm
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The 3 sections of a game spinner are numbered 1 to 3. Which tree diagram shows all the possible outcomes for 2 spins?
The tree diagram shows all the possible outcomes for 2 spins C is correct.
We have given that,
The 3 sections of a game spinner are numbered 1 to 3.
We have to determine, which tree diagram shows all the possible outcomes for 2 spins.
There are 3 options the first time and after that,
There are 3 options for each of those.
So it would be C.
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Given: ΔPSQ, PS = SQ PΔPSQ = 50 SQ – PQ = 1 Find: Area of ΔPSQ
Please help I don't understand, if you can please show work, thank you
25 percent of the workers are on third shift.there are 33 workers on third shift. how many workers are there total?
you deposit 100$ each month into an account earning 8% interest compounded monthly. How much will you have in the account in 15 years
You would have approximately $448.68 in the account after 15 years.
To calculate the amount in the account after 15 years, compounded monthly at 8% interest, you can use the formula for compound interest:A=P×(1+r/n)^ntWhere:
A is the future value of the investment,
P is the principal amount (initial deposit),
r is the annual interest rate (as a decimal),
n is the number of times interest is compounded per year, and
t is the time the money is invested for in years.
Here,
P=100,r=0.08,n=12 (compounded monthly), and t=15 years.
A=100×(1+0.08/12)^12×15
A=100×(1+0.08/12)^180
A=100×(1+120.08)^180
A=100×(1+0.08/12)^180
A≈100×(1.00666667)^180
A≈100×4.48678
A≈448.678
Complete question:
you deposit 100$ each month into an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?
krista bought 6 gallons of gasoline and paid $6.89. to the nearest tenth of a cent, what is the price of gasoline per gallon
The price per gallon of gasoline is the cost of one gallon of gasoline which can be obtained by dividing the cost by the number gasoline purchased. Hence, the price per gallon of gasoline ls $1.15
Amount of gasoline purchased = 6 gallons
Total cost = $6.89
The price per gallon of gasoline can be calculated thus :
Total cost of gasoline ÷ Amount of gasoline purchasedPrice per gallon = $6.89 ÷ 6 = $1.148
Therefore, the price per gallon of gasoline ls $1.15 (rounded to the nearest tenth)
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What is the experimental probability of the arrow stopping over section 2?
Which is greater 17/20 or 22/25
A rectangular wall has a length of 12 ft and a width of 8 ft. The wall has two rectangular windows. Each window has a width of 3 ft and a height of 5 ft. Andrea chooses a point on the wall at random to test a new paint color. What is the probability she could choose a point on a window? Enter your answer, as a decimal rounded to the nearest hundredth, in the box. P(choosing a point on a window) = The figure shows two rectangles inside a larger rectangle. The two smaller rectangles each have a length of 3 feet and a width of 5 feet. The larger rectangle has a length of 12 feet and a height of 8 feet.
Answer:
the frst guy is right go dude your rock i love bing suportive!!
Step-by-step explanation:
Solve.
2x^2 + x - 1 = 2
A 1,2
B No real solutions
C 1,-3/2
D x = (-1 plus minus 3) over 2
[tex]2x^2+x-1=2\ \ \ |-2\\\\2x^2+x-3=0\\\\2x^2+3x-2x-3=0\\\\x(2x+3)-1(2x+3)=0\\\\(2x+3)(x-1)=0\iff 2x+3=0\ \vee\ x-1=0\\\\2x+3=0\ \ |-3\\2x=-3\ \ \ |:2\\x=-\frac{3}{2}\\\\x-1=0\ \ \ |+1\\x=1[/tex]
Answer: C 1, -3/2
How is the expression (5 + y) ⋅8 described by its factors and terms?
A) It has two factors and the factor (5 + y) has one term.
B) It has three factors and the factor (5 + y) has one term.
C) It has three factors and the factor (5 + y) has two terms.
D) It has two factors and the factor (5 + y) has two terms.
The speed that a tsunami (tidal wave) can travel is modeled by the equation where S is the speed in kilometers per hour, and d is the average depth of the water in kilometers. A tsunami is traveling at 140 km/hr. What is the approximate average depth of the water?
Answer:
The average depth of the water will be 0.155 kilometers or 155 meters.
Step-by-step explanation:
The speed at which the tsunami waves travel is [tex]S=356\sqrt{d}[/tex]. Here S is the speed in kilometers per hour and d is the average depth of the water in kilometers.
Now, it is given that the wave travels at the speed of [tex]S=140\rm km/hr[/tex].
So, the average depth of the water will be,
[tex]S=356\sqrt{d}\\140=356\sqrt{d}\\\sqrt{d}=0.393\\d=0.155\rm km[/tex]
Therefore, the average depth of the water will be 0.155 kilometers or 155 meters.
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Answer: c
Step-by-step explanation:
0.155 km
Math- finding the volume of the triangle. Please show work, I am very confused
Plzzz help
what is the mean for the data set 582, 505, 548, 578, 511, 506, 521, 546, 570. express your answer as a decimal to the nearest tenth
yesterday, noah ran 2 1/2 miles in 3/5 of an hour. Emily ran 3 3/4 miles in 5/6 hour. Anna ran 3 1/3 in 3/5 hour. How fast, in miles per hour l, did each person run? who ran the fastest?
Evan earns $12 an hour plus $15 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week.
Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime.
Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours.
Part C: Evan earned $510 in 1 week. How many hours (regular plus overtime) did he work? Show your work.
Extra Credit (3 points): Try this with actual dough (playdoh, homemade dough, clay). Form a cube. Consider the cross sections that are formed when you slice into the cube as described. Draw each slice and describe the resulting cross section. A slice through the center, parallel to a side. A slice that cuts through the left top edge and the right bottom edge. A slice that cuts across a corner through three sides of the cube. Describe in a paragraph your observations and reflections.
Janet's gross salary is $2400 per month, what is her gross yearly salary
What fraction makes the equation true?
2/3 x blank = 8/12
HELP!
What is Jacobson's conjecture?
What sequence of transformations, when applied to △ABC , shows that △ABC is similar to △A′B′C′ ?
dilation with respect to the origin by a scale factor of 2 followed by a translation of 2 units left
dilation with respect to the origin by a scale factor of 12 followed by a translation of 2 units right
translation of 2 units right followed by a dilation with respect to the origin by a scale factor of 12
translation of 2 units left followed by a dilation with respect to the origin by a scale factor of 12
The correct sequence of transformations that shows that △ABC is similar to △A′B′C′ is:
translation of 2 units left followed by a dilation with respect to the origin by a scale factor of 12.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object.
In this case, we can see that a dilation with respect to the origin by a scale factor of 12 would stretch or shrink the triangle, but would not change the angles.
Therefore, we need to apply a translation first to move the triangle into the correct position.
So, we first translate the triangle 2 units left, which does not change its shape or size, but moves it to a position where it can be more easily compared to the other triangle.
Then, we apply a dilation with respect to the origin by a scale factor of 12, which stretches or shrinks the triangle but does not change its shape.
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Estimate x- and y- intercepts of the graph
Which relations represent functions ?
Answer: First and third
Step-by-step explanation:
A function is a special kind of relation between two variable such that each input corresponds to exactly one output.In the given pictures, the first and third picture are representing function because each input corresponds to exactly one output.
In second and fourth picture one input value corresponds to two output values.
i.e. a corresponds to 25 and 55 and x corresponds to 7 and 5 in output.
PLEASE HELP! In college, you earn credits for courses taken. For each semester, tuition at a local college is $2400, plus $184 per credit. You have financial aid that will cover $5,160 for the semester. How many credits can you take without spending any of our own money?
Out of 40 coins, 16 are dimes. Half of the remaining coins are quarters and the rest are pennies and nickels. There are 2 nickels for every penny. How many pennies are there?
Answer:
Option (B) is correct, 4 pennies.
What series of transformations map triangle △ABC onto △EDF to prove that ABC≅EDF ?
translation 3 units up then a reflection across x-axis
translation 3 units down then a reflection across y-axis
translation 3 units down then a reflection across x-axis
translation 3 units up then a reflection across y-axis
Answer:
translation 3 units down then a reflection across x-axis
Step-by-step explanation:
A translation is a kind of rigid motion . It trace a function that maps an object a particular distance.A reflection is a kind of rigid motion . It is mainly a flips of a shape across the line of reflection.In the given figure, we can see that Δ ABC is vertically 3 units away from the x axis .
So we translate Δ ABC by 3 units down and then reflect it across x axis to get ΔDEF.
bloomingdale's marks up mink coats $3000.this represents a 50% markup on cost. What's the cost of coats
Bloomingdale's marks up mink coats [tex]\[/tex]3000. The mink coats cost [tex]\[/tex]6000.
Cost, in the context of pricing and business, refers to the amount of money or resources required to produce or acquire a product or service. It contains several expenses associated with manufacturing, production, materials, labor, overhead costs, and other costs incurred in the process.
Let's assume the cost of the mink coats is represented by the variable "C".
According to the given information, Bloomingdale marks up the mink coats by [tex]\[/tex]3000, which represents a 50[tex]\%[/tex] markup on the cost.
A 50[tex]\%[/tex] markup means the markup amount is 50[tex]\%[/tex] of the cost. In other words, the markup amount is 0.5C.
Let's set up the equation to represent this information,
C + 0.5C = Cost + Markup
1.5C = Cost + [tex]\[/tex]3000
Since the markup is $3000, we can write the equation as,
1.5C = C + [tex]\[/tex]3000
To find the cost of the coats, it is needed to solve for C.
1.5C - C = C - C + [tex]\[/tex]3000
0.5C = [tex]\[/tex]3000
Next, let's isolate C by dividing both sides of the equation by 0.5,
[tex]\frac{0.5C}{ 0.5}[/tex] = [tex]\frac{3000}{0.5}[/tex]
C = [tex]\[/tex]6000
Therefore, the cost of the mink coats is [tex]\[/tex]6000.
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